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Processes occurring within small areas (patch-scale) that influence species richness and spatial heterogeneity of larger areas (landscape-scale) have long been an interest of ecologists. This research focused on the role of patch-scale deterministic chaos arising in phytoplankton assemblages characteristic of “Rock-Paper-Scissors” population dynamics (i.e., competitively non-hierarchical). We employed a simple 2-patch model configuration with lateral mixing and through-flow, and tested the robustness of species richness at the scale of the landscape and spatial heterogeneity. Three different assemblages were used that in a dimensionless box model configuration exhibited chaotic behavior. Our results showed that when a spatial dimension was added to the model configuration, and when all species were shared between patches (i.e., no invading populations), chaos-induced species richness and spatial heterogeneity were quickly reduced with the onset of mixing. While assemblages in each patch were comprised of exactly the same species, they differed in their proportional population densities due to differing stages of succession and the incidence of alternative assemblage structures. Even at very low mixing rates (0.001d−1), which produced low passive migration rates (0.1% of the total biomass per day), the incidence of high richness and heterogeneity decreased by ∼80%. Interestingly, this sensitivity was not the same for the three assemblages tested. Declines in species richness and spatial heterogeneity associated with mixing were greater in assemblages comprised of competitively dissimilar species (based on the area occupied in the resource-tradeoff space defined by the R* model). The underlying mechanisms may involve the degree to which nutrient dynamics are altered with the arrival of immigrants. Our findings suggest that in partially to well-mixed aquatic systems, the roles of patch-scale non-hierarchical competition and chaos as factors maintaining species richness and spatial heterogeneity may be limited. However, in aquatic systems that experience periods of very low mixing, or even disconnection, non-hierarchical competition and chaos might indeed contribute significantly to biodiversity. [Copyright &y& Elsevier]

• Constructing pseudo-Hamiltonian system, the topology of dynamic motion is able to distinguish whether the system is in chaos. • The fractal process of the attraction basin verifies the chaotic distribution solved by Melnikov function. • Larger force fluctuation leads to the critical point hysteresis of damping and average force occurring bifurcation or chaos. • The quantitative optimal couple of structural with process parameters determine the priority of the parameter control. This paper investigates the stability of horizontal nonlinear vibration of four-high cold mill under the effects of gyro-precession and eccentricity between rolls. The threshold value of chaos about Smale horseshoe commutation is given from Melnikov method, and the correctness of the result is verified by the fractal process of the attraction basin. Through the analyzes of bifurcation, maximum Lyapunov exponents and bi-parameter bifurcation, it is revealed for the effect of different parameters variation on the nonlinear dynamic behavior of horizontal vibration in rolling system. The results show, the fluctuation amplitude of horizontal force increases, the stable domain decreases, and once its value ≥3.5, it is necessary to prefer to the adjustment of parameter-exciting stiffness; meanwhile, it is noticeable that the critical points of damping and average force of the system with bifurcation or chaos appear hysteresis. The evolutions of system dynamics with four pairs of parameter changes confirm the quantitative optimal couple of one structural plus one process parameter in the system. Based on this, we can also find a balance between the average horizontal force and eccentricity, so as to optimize the structural design so that there is a proper and reliable eccentricity between the rolls. The results provide a theoretical reference for service stability and dynamic reliability of the rolling mill system. [ABSTRACT FROM AUTHOR]

Abstract: In the commented paper the authors consider a model of a two-dimensional airfoil with cubic nonlinearity in supersonic flow. They claim to prove the existence of Siʼlnikov homoclinic orbits by using the undetermined coefficient method and, consequently, Smale horseshoe chaos occurs via Siʼlnikov criterion. Unfortunately, their demonstration is invalid because the form of the function they assume in the series expansion for the homoclinic orbits is incorrect. Namely, they compose the homoclinic orbit of the same manifold, which is stable in forward time and unstable in reverse time. [Copyright &y& Elsevier]

This paper studies the synchronization behavior of multistable chaotic systems with coexisting symmetric attractors. Specifically, the focus is on the attractive and repulsive couplings of the attractors in single-variable couplings. It is shown that in the self-couplings, both attractors have the same synchronization pattern either in the attractive or repulsive coupling. In the cross-couplings, the synchronization pattern of the attractors is dependent on the variables involved in the coupling and the symmetry transformation. If the coupling scheme is defined such that only one of the variables in the coupling participates in the symmetry transformation, the synchronization patterns of the symmetric attractors are symmetric in the attractive and repulsive couplings. The master stability function is applied to four chaotic systems with different symmetry transformations to represent the results. The corresponding chaotic circuit of two coupled symmetric systems is also implemented and their symmetric responses are shown. • Synchronization stability of coexisting symmetric chaotic attractors is investigated. • Coupling is considered to be both attractive and repulsive through single variable. • In self-couplings, symmetric attractors have the same synchronization patterns. • symmetry synchrony is observed if one transformation variable is in the coupling. [ABSTRACT FROM AUTHOR]

[Display omitted] • Shape and size Optimization of truss Structures is considered. • Chaos Game Optimization (CGO) is utilized for optimization purposes. • Benchmark 10-bar, 37-bar, 52-bar, 72-bar and 120-bar truss structures are utilized. An engineering system consists of properly established activities and put together to achieve a predefined goal. These activities include analysis, design, construction, research, and development. Designing and constructing structural systems, including buildings, bridges, highways, and other complex systems, have been developed over the centuries. However, the evolution of these systems has been prolonged because the overall process is very costly and time-consuming, requiring primary human and material resources to be utilized. One of the options for overcoming these shortcomings is the utilization of metaheuristic algorithms as recently developed intelligent techniques. These algorithms can be utilized as upper-level search techniques for optimization procedures to achieve better results. Shape and size optimization of truss structures are considered in this paper utilizing the Chaos Game Optimization (CGO) as one of the recently developed metaheuristic algorithms. The principles of chaos theory and fractal configuration are considered inspirational concepts. For the numerical purpose, the 10-bar, 37-bar, 52-bar, 72-bar, and 120-bar truss structures as four of the benchmark problems in this field are considered as design examples in which the frequency constraints are considered as limits that have to be dealt with during the optimization procedure. Multiple optimization runs are also conducted for having a comprehensive statistical analysis, while a comparative investigation is also conducted with other algorithms in the literature. Based on the results of the CGO and other approaches from the literature, the CGO can provide better and competitive results in dealing with the considered truss design problems. In summary, the CGO can provide better solutions in dealing with the considered real-size structural design problems with higher levels of complexity. [ABSTRACT FROM AUTHOR]

Nonlinear kinetic energy harvesters are becoming more and more popular as well as advanced and efficient. This paper presents the study of the dynamics of such a system in a wide range of excitation parameters, assuming at the same time the possibility of a cyclical and smooth change of the potential function. We have designed a system that allows to obtain a wide spectrum of potential characteristics, from a single well to a three-well system, and we have analyzed its effectiveness. Next, we checked the influence of parameters characterizing the change of potential using bifurcation diagrams and their comparison with the effective voltage values. We also analyzed the behavior of the system in chaotic and periodic motion zones and presented selected sections of Poincare and Fourier amplitude-frequency spectra of chaotic solutions. The last element of the analysis was the impact of cyclic potential change on coexisting solutions. We have shown that the best effectiveness is achieved when the frequency of the external load is equal to the resonant frequency of the flexible cantilever beam and the change of potential is limited to extreme positions. • A new way of the potential function dynamic change in EH was proposed. • EH effectiveness analysis was made for chaotic and periodic motion zones. • Influence of the range and frequency of potential changes on the dynamics of the system was checked. [ABSTRACT FROM AUTHOR]

The accurate prediction of digging load serves as a fundamental cornerstone for advancing the development of intelligent and unmanned excavators. Given the complex nonlinear dynamics of digging load, this paper proposes a novel prediction model for excavator load power based on the chaos theory and support vector regression (SVR). The presence of chaos in the dynamic digging load system is detected through phase space reconstruction. SVR is utilized for nonparametric modeling and prediction, with the reconstructed phase space capturing the essential characteristics of excavator load and serving as inputs for SVR. To optimize the hyperparameters, an improved particle swarm optimization (IPSO) algorithm is presented. Excavation experiments conducted under two typical load conditions demonstrate the superiority of the proposed chaos-based IPSO-SVR model in terms of prediction accuracy. This research lays a solid foundation for practical load prediction in industrial excavator settings. [ABSTRACT FROM AUTHOR]

Synchronization of satellite systems offers numerous advantages, including cost-effectiveness, flexibility, and extended area coverage. However, the presence of chaotic behavior in such systems poses substantial challenges. This paper investigates chaos in satellite systems and proposes a novel approach - the Novel Integral Terminal Sliding Mode (NITSM) controller - specifically designed for synchronizing the angular velocities of chaotic Leader-Follower satellite systems. The NITSM controller leverages limited-time features to eliminate chattering and exhibits remarkable robustness against external disturbances such as cosmic rays and solar storms. MATLAB simulations are conducted to validate the effectiveness of the proposed method, comparing the synchronization error of the NITSM controller with a common approach. The results demonstrate the superior performance of the Novel Integral Terminal Sliding Mode controller, showcasing reduced response time, robust behavior, and a substantial six-fold reduction in angular velocity synchronization error. [ABSTRACT FROM AUTHOR]

This paper deals with the attitude motion of LEO satellites with deployable side panels designed for passive aerodynamic stabilization in a rarefied atmosphere. The influence of the aerodynamic and gravitational torques on the planar attitude motion near the unstable and stable equilibrium positions is studied. The presence of the unstable equilibrium position and small perturbations such as the oscillations of the flexible panels is the cause of chaos. A critical altitude is found above which the chaos is possible. The equations of planar attitude motion of the satellite with deployed flexible panels are obtained. The chaotic behavior of the system is demonstrated through numerical simulations of the attitude motion of a 3U CubeSat. The results of this paper can be used to analyze the applicability of passive aerodynamic stabilization for LEO satellites. • Planar attitude motion of a LEO satellite with deployable side panels is studied. • The satellite as a rigid body with the flexible appendages is considered. • For a wide range of altitudes, stable and unstable equilibrium positions are found. • The chaotic behavior of the satellite with flexible panel is proven. • It's been shown that flexible panels do not always lead to stabilization of motion. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional conservative system is proposed. By analyzing the Hamiltonian energy, it is concluded that it is a non-Hamiltonian conservative system. By changing the values of the parameters b, c, the system presents different attractors. Then, by studying the multiple attractors coexisting of the system under different initial values, it can be found that the system has rich coexistence phenomena by changing the parameters. There are various types of coexistence of systems with chaos and chaos coexistence, periods and periods coexistence and chaos and periods coexistence. In addition, the offset-boosting under parameter control is studied by phase diagram. By studying the complexity of the system at two different initial values, the more complex initial value is chosen as the initial state when the system is synchronized. The analog simulation circuit is implemented using Multisim, the actual digital circuit is implemented with field programmable gate array (FPGA). The Matlab phase diagram, the numerical simulation results and the simulated circuit all agree well, proving the feasibility of the new system. Finally, the system is applied to backstepping synchronization, which lays a foundation for the realization of engineering application. • In this paper, a three-dimensional conservative system is proposed. It is proved to be a non-Hamiltonian three-dimensional conservative system by Hamiltonian energy analysis. • Successful implementation of Multisim simulation and FPGA hardware proved the feasibility of the system. • Through a series of studies, it has been found that conservative systems are more conducive to confidential communication. Therefore, based on this 3D conservative system, the system is applied to backstepping synchronization. [ABSTRACT FROM AUTHOR]

The existence and identification of chaos regarding in-plane pitch motions of tethered satellite systems are scientific problems of concern, and are directly related to normal system operations in the station-keeping phase. This paper studies the effect of microamplitude longitudinal oscillation on the occurrence of chaos in a tethered system subjected to atmospheric perturbations. Based on a simplified rod model that considers tether elasticity and satellite masses, the Melnikov method is used to identify a criterion that can predict chaos, and a chaotic zone is further proposed to recognize the relationship between the chaos and system parameters. Then the cell mapping method is used to describe the system's global dynamic behaviors, including chaos. A discrete model of the flexible system that consists of particles connected by massless springs and satellite rigid bodies is structured so that more accurate dynamic simulations can be used to verify the theoretical analysis. Finally, numerical examples demonstrate that the chaotic zone and criterion expression are useful tools for revealing chaos. The relationship between the dynamics and system parameters is also assessed. The results of the simplified model agree with those of the sophisticated model. • A chaotic criterion and a chaotic zone on a tethered satellite system are proposed. • The relationship between the dynamics and system parameters is estimated. • The global dynamic characteristics of the system are revealed via cell mapping. [ABSTRACT FROM AUTHOR]

In this paper, a multiscroll snap oscillator with hyperbolic tangent function is proposed. There is no limitation in the number of scrolls and it can be increased by proper choice of a specific function. The Lyapunov exponents of the proposed system are obtained to testify the chaotic behavior of the system. Fractional order multiscroll system is derived from its integer order model by using the Adams–Bashforth–Moulton algorithm. A new scheme is applied in order to investigate the synchronization of the multiscroll systems. The main objective of the paper is to propose a multiscroll attractor and show that the number of scrolls can be controlled by the only nonlinear function. Such systems are less investigated in the literatures and has many real time applications like image and voice encryption, random number generators, chaos based communication systems and so on. • We propose a multiscroll snap oscillator with hyperbolic tan function. • We have demonstrated generating up to five scrolls but not limited to five. The number of scrolls may be increased by proper choice of the multiscroll function. • Fractional order multiscroll system is derived from its integer order model using the Adams-Bashforth-Moulton algorithm. • A new synchronization scheme is derived and presented to synchronize the multiscroll systems. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, a description and mathematical analysis of a simple model of nonlinear pattern formation is given. The model is based on the so-called activator-inhibitor system proposed by Thomas. We introduce time delay into the reaction term and focus on its influence on morphogenesis and pattern formation. Numerical simulations are presented and compared for both cases without and with delay. [Copyright &y& Elsevier]

• We propose and analyse a delayed nonautonomous predator-prey model with disease in prey. • Derived the sufficient conditions for global asymptotic stability of the positive periodic solutions. • Autonomous system develops only limit cycle oscillations through a Hopf-bifurcation for increasing the values of delay. • Corresponding nonautonomous system shows chaotic dynamics for increasing the delay parameter. • We draw Poincare map and maximum Lyapunov exponent to identify the chaotic behaviour of the system. In this paper, we propose and analyze a nonautonomous predator-prey model with disease in prey, and a discrete time delay for the incubation period in disease transmission. Employing the theory of differential inequalities, we find sufficient conditions for the permanence of the system. Further, we use Lyapunov's functional method to obtain sufficient conditions for global asymptotic stability of the system. We observe that the permanence of the system is unaffected due to presence of incubation delay. However, incubation delay affects the global stability of the positive periodic solution of the system. To reinforce the analytical results and to get more insight into the system's behavior, we perform some numerical simulations of the autonomous and nonautonomous systems with and without time delay. We observe that for the gradual increase in the magnitude of incubation delay, the autonomous system develops limit cycle oscillation through a Hopf-bifurcation while the corresponding nonautonomous system shows chaotic dynamics through quasi-periodic oscillations. We apply basic tools of non-linear dynamics such as Poincaré section and maximum Lyapunov exponent to confirm the chaotic behavior of the system. [ABSTRACT FROM AUTHOR]

• New Chaotic bridging mechanism is proposed for Grasshopper Optimisation algorithm. • Chaotic Crossover scheme is proposed. • Implications of the modification on performance of algorithm are validated on CEC-2017. • Various analyses are presented to validate the proposed approach. • Real applications of proposed variants are reported on challenging problems. In recent years, the trend of embedding chaos in the optimization algorithms has grown multifold. Usually, the chaotic algorithms employ chaotic sequences instead of random numbers, in the exploration phase or they employ chaotic numbers for decision making in the exploitation phase. In literature, the positive impact of chaos over the performance of algorithms have been studied and reported. However, very little work is reported on the implications of chaos on the bridging mechanism between the exploration and exploitation phases. This paper presents implications of different chaotic sequences on the performance of Grasshopper Optimisation Algorithm (GOA). A bridging mechanism based on sinusoidal truncated function is proposed first, then 10 different normalize chaotic sequences are employed with this function. Along with this bridging mechanism, a chaotic operator derived crossover scheme is also proposed. These experiments evolve 11 different variants of GOA. The proposed modifications maintain an effective balance between exploration and exploitation phases. Simultaneously, it reduces the attraction, repulsion and comfort zone chaotically. New variants are benchmarked on latest 29 Congress on Evolutionary Computation-2017 (CEC-2017) functions. Efficacy of these variants is validated with several statistical tests and plots. Further, some real life challenging problem of engineering domain are considered for evaluating the efficacy of the proposed variants. These problems are Model Order Reduction (MOR) of control engineering, Protein Structure Prediction (PSP) of bio informatics and Frequency Modulated Sound Wave Parameter Synthesis Problem of parameter estimation. Results reveal that proposed variants exhibit better exploration and exploitation properties as compared to the parent algorithm. [ABSTRACT FROM AUTHOR]

Uncertainty Quantification (UQ) employing a Monte Carlo Sampling (MCS) method in a building simulation domain has been widely used to account for risks of predicted outputs for robust decision making. However, the stochastic approach for UQ problems requires significant computational burdens compared to the deterministic approach. This paper addresses two surrogate models (Gaussian Process Emulator (GPE) and Polynomial Chaos Expansion (PCE)) which together can be regarded as a meta-model of a Building Performance Simulation (BPS) tool with a high-fidelity model. In the paper, the developed GPE and PCE with different model structures were compared in terms of a prediction capability under different amount of training data and number of inputs. The aim of the comparative study is to identify the relative prediction abilities and model flexibility of GPE and PCE. It was found that the GPE and PCE produce high performance qualities having fast computation speed compared to the developed basis model if new inputs having identical inputs and probability ranges were used. In terms of two-sample Kolmogorov-Smirnov (K-S) hypothesis test, mean values of the minimum p-values of the GPE and PCE were 0.999 and 0.569, respectively, if the number of samplings are over 30 cases. Otherwise, the PCE shows significantly reduced performance quality than the GPE. [ABSTRACT FROM AUTHOR]

Process planning and scheduling are two of the most important manufacturing functions traditionally performed separately and sequentially. These functions being complementary and interrelated, their integration is essential for the optimal utilization of manufacturing resources. Such integration is also significant for improving the performance of the modern manufacturing system. A variety of alternative manufacturing resources (machine tools, cutting tools, tool access directions, etc.) causes integrated process planning and scheduling (IPPS) problem to be strongly NP-hard (non deterministic polynomial) in terms of combinatorial optimization. Therefore, an optimal solution for the problem is searched in a vast search space. In order to explore the search space comprehensively and avoid being trapped into local optima, this paper focuses on using the method based on the particle swarm optimization algorithm and chaos theory (cPSO). The initial solutions for the IPPS problem are presented in the form of the particles of cPSO algorithm. The particle encoding/decoding scheme is also proposed in this paper. Flexible process and scheduling plans are presented using AND/OR network and five flexibility types: machine, tool, tool access direction (TAD), process, and sequence flexibility. Optimal process plans are obtained by multi-objective optimization of production time and production cost. On the other hand, optimal scheduling plans are generated based on three objective functions: makespan, balanced level of machine utilization, and mean flow time. The proposed cPSO algorithm is implemented in Matlab environment and verified extensively using five experimental studies. The experimental results show that the proposed algorithm outperforms genetic algorithm (GA), simulated annealing (SA) based approach, and hybrid algorithm. Moreover, the scheduling plans obtained by the proposed methodology are additionally tested by Khepera II mobile robot using a laboratory model of manufacturing environment. [ABSTRACT FROM AUTHOR]

Abstract In this paper we generalize the notion of an unpredictable point in a semiflow, introduced by Akhmet and Fen in 2016, to the case of semiflows with arbitrary acting topological monoids. We then introduce the notions of strong Ruelle–Takens and strong Auslander–Yorke chaoticity in semiflows. We use unpredictable points in some statements involving these notions. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a novel three-dimensional fractional-order chaotic system without linear terms is proposed. Compared with other similar fractional-order chaotic systems, this system has two striking and unique features: (i) it exhibits robust chaotic behavior (i.e., sustained chaotic behavior) with respect to parameter b and more interestingly, the corresponding largest Lyapunov exponent becomes increasingly big with the increase of the parameter b ; (ii) it can generate two twin symmetric strange attractors when the simulation time is reversed. To our knowledge, such a three-dimensional fractional-order chaotic system holding these two special features simultaneously has never been reported. Using standard nonlinear dynamical analysis tools including phase portraits, equilibrium stability, Poincaré map, bifurcation diagram, Lyapunov exponents and spectral entropy complexity, the complex dynamical behaviors of the system are systematically analyzed and investigated. And the complexity results well matches with that of the bifurcation diagrams, showing complexity can well reflect the dynamical properties of this fractional-order chaotic system. Furthermore, to validate the correctness and practical feasibility of the system under study, hardware electronic circuits with different fractional orders are designed. And the corresponding experimental results are also presented to confirm the theoretical analysis. Highlights • A novel three-dimensional fractional-order chaotic system without linear terms is proposed. • The system exhibits robust chaotic behavior with respect to one of system parameters. • The system generates two twin symmetric strange attractors when time is reversed. • Hardware circuits with different fractional orders are designed to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

Highlights • Transition from laminar to chaotic natural convection is analyzed. • Oscillations and bifurcations of nature convection are studied. • Effect of four configurations on instability of natural convection are studied. • The flow is more unstable with the larger slotted ratio. Abstract The characteristics of transition from laminar to chaotic natural convection in a two-dimensional horizontal annulus with an internally slotted circle is analyzed using Lattice Boltzmann method (LBM). The aim of this paper is to identify the route(s) to chaos, and to illustrate the dynamical response of the flow with the change of the control parameter (Ra). The results obtained for a range of the Rayleigh number, Ra , from 5 × 103 to 2 × 106 at Pr = 0.71, and the slot degree, S f , from 0.1 to 0.4. The numerical results show that slot ratio, slot configuration, and Rayleigh number are influential to oscillation phenomenon in this model; the flow inside the annulus may be: (1) a stable base-two-cells regime, (2) a multi-cellular flow with four-stable-symmetrical-secondary cells regime, (3) a multi-cellular flow with four-oscillatory-secondary cells regime, and (4) an asymmetrical oscillation regime. The results also show that the oscillatory flow undergoes several bifurcations and ultimately evolves to a chaotic flow after the first bifurcation. In addition, certain features of nonlinear dynamical systems like bifurcation, self-sustained oscillations are also observed. The simulation results also show that slot degree S f is relevant to oscillations. Furthermore, with the larger slotted ratio, the flow is more unstable, and the configuration with top and bottom slot seems to be the most unstable among the given four models. [ABSTRACT FROM AUTHOR]

Highlights • The dynamic responses of a bit-rock system with both the linear and nonlinear interaction models are verified as similar. Hence, the linear model is suggested to predict the system dynamics due to its higher computing efficiency. • An isola of period-doubling bifurcations is observed during two-parameter continuation, and the isola is formed via two turning points which lie on its left and right endpoints. • As the increase of either excitation amplitude or static force, the ROP of the stable period-one motion can be promoted almost linearly. While, the increase of excitation frequency will lead to a nonlinear decrease of the ROP. Graphical abstract Abstract This paper presents a comprehensive numerical study of a higher order drifting oscillator that has been used to model vibro-impact drilling dynamics in previous publications by our research group [1,2,3,4,5,6,7,8,9]. We focus on the study of the bit-rock interactions, for which both linear and nonlinear models of the drilled medium are considered. Our investigation employed a numerical approach based on direct numerical integration via a newly developed MATLAB-based computational tool, ABESPOL (Chong et al., 2017) [10], and based on path-following methods implemented via a software package for continuation and bifurcation analysis, COCO (Continuation Core) (Dankowicz and Schilder, 2013) [11]. The analysis considered the excitation frequency, amplitude of excitation and the static force as the main control parameters, while the rate of penetration (ROP) was chosen as the main system output so as to assess the performance of the system when linear and nonlinear bit-rock impact models are used. Furthermore, our numerical investigation reveals a rich system dynamics, owing to the presence of codimension-one bifurcations of limit cycles that influence the system behaviour dramatically, as well as multistability phenomenon and chaotic motion. [ABSTRACT FROM AUTHOR]

Measuring the color tuning of visual neurons is important for understanding the neural basis of vision, but it is challenging because of the inherently three-dimensional nature of color. Color tuning cannot be represented by a one-dimensional curve, and measuring three-dimensional tuning curves is difficult. One approach to addressing this challenge is to analyze neuronal color tuning data through the lens of mathematical models that make assumptions about the shapes of tuning curves. In this paper, we discuss the linear-nonlinear cascade model as a platform for measuring neuronal color tuning. We compare fitting this model by three techniques: two using response-weighted averaging and one using numerical optimization of likelihood. We highlight the advantages and disadvantages of each technique and emphasize the effects of the stimulus distribution on color tuning measurements. [ABSTRACT FROM AUTHOR]

Borel and Reutenauer (2006) [3] showed, inter alia , that a word w of length n > 1 is conjugate to a Christoffel word if and only if for k = 0 , 1 , … , n − 1 , w has k + 1 distinct circular factors of length k . Sturmian words are the infinite counterparts to Christoffel words, characterized as aperiodic but of minimal complexity, i.e., for all n ∈ N there are n + 1 factors of length n . Berthé (1996) [2] showed that the factors of a given length in the Sturmian case have at most three frequencies (probabilities). In this paper we extend to results on factors of both Christoffel words and Sturmian words under fixed partitionings (decompositions of factors of length m into concatenations of words whose lengths are given by a composition of m into k components). Any factor of a Sturmian word (respectively, circular factor of a Christoffel word) thus partitioned into k elements belongs to one of k + 1 equivalence classes (varieties). We show how to compute the sizes of the equivalence classes determined by a composition in the case of Christoffel word, and show how to compute the frequencies of the classes in the case of Sturmian words. A version of the finitary case was proved in a very different context (expressed in musical and number-theoretical terms) by Clough and Myerson (1985, 1986) [5,6] ; we use their terminology, variety and multiplicity . [ABSTRACT FROM AUTHOR]

Little seems to be known about the chaotification control of fractional order linear and nonlinear systems. This paper proposes a novel chaotification method for fractional order nonlinear systems based on the negative damping instability mechanism and fractional calculus technique. We then apply it to chaotify the fractional order Lorenz system with order lying in ( 1 , 2 ) , which is stable originally with specific parameters. Moreover, we introduce three critical effective orders to distinguish different four dynamics: singleton sets attractor, self-excited attractor, coexisting attractors, and blow up behavior. Many simulations are carried out to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Most non-destructive ultrasonic automatic scanning tests are programmed with a complete systematic trajectory. However, when the location of a discontinuity (disturbance source) and the searching space are unknown, an exhaustive search can be time and computational inefficient. In this paper, the efficiency of chaotic trajectories to search for a discontinuity in an area with limited information is studied. The probability of detection and its relationship with topological properties of the proposed chaotic dynamic model is analyzed. The Pearson’s random walk model is modified to substitute random for chaotic behavior by transferring the solutions of the chaotic dynamical model to the phase and modulus of the discrete path trajectories. This provides a simple description of the trajectories in a vector space where only magnitude and phase are required. Following this approach, the chaotic trajectories were generated in the working plane and then transferred to a Cartesian robotic ultrasonic system. The system was tested without human supervision on unknown environments for ultrasonic detection of hidden defects. The results show that the studied chaotic walk model provides efficient ultrasonic scanning trajectories for defect detection and can outperform systematic scanning when the geometry of the workspace is complex and unknown. [ABSTRACT FROM AUTHOR]

In this participation we discuss the possibility of mutual fusion of evolutionary algorithms and deterministic chaos. As demonstrated in previous research papers, evolutionary algorithms are capable of chaotic system control, identification or synthesis and vice versa, chaos can be observed in the evolutionary dynamics. More exactly, in this paper there is numerically demonstrated possible solution of the question whether identification of so-called basin of attraction for hidden attractor can be done by evolutionary algorithms. Hidden attractors are a special kind of attractors, that are hidden in the system structure and if ignored (undiscovered), then can cause serious damages, as already observed in the real world. The research presented here is bivalent. At first it shows, that evolutionary algorithms are able to identify presence of hidden attractors in the system, but also it can be extended to study an existence of hidden attractors in the evolutionary algorithms dynamics. All numerical simulations are demonstrated on Chua׳s chaotic attractor that contains an example of hidden attractor and at the end there are discussed discrete systems (synthesized by evolution) that likely exhibit hidden attractors, too. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of robust fault detection using recurrent neural networks and chaos engineering. The main part of the proposed approach is a locally recurrent neural network that is composed of complex dynamic neural units for which chaotic behaviour can be obtained. Selected global and local optimization methods are connected to have diphase strategies for training this kind of neural networks. And beyond this, chaos engineering is incorporated into both the evolutionary and simulated annealing algorithm in order to improve the efficiency of the tuning procedure. The problem of selecting the most relevant input variables is solved by means of extended Hellwig׳s method of integral capacity of information. Criteria isolines and a sensitive-based method are used to identify the suitable architecture of a neural network. Moreover, the issue of stability analysis of neural models is also considered in this paper. Recurrence quantification analysis is proposed for residual evaluation in order to have the comprehensive methodology of neural model-based fault detection. The preliminary verification of the elaborated methodology in modelling tasks was carried out for both simulation and industrial data. The fundamental verification was conducted for the data made available within DAMADICS benchmark problem. The achieved results confirm the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper we investigate the bifurcations and the chaos of a piecewise linear discontinuous (PWLD) system based upon a rig-coupled SD oscillator, which can be smooth or discontinuous (SD) depending on the value of a system parameter, proposed in [18] , showing the equilibrium bifurcations and the transitions between single, double and triple well dynamics for smooth regions. All solutions of the perturbed PWLD system, including equilibria, periodic orbits and homoclinic-like and heteroclinic-like orbits, are obtained and also the chaotic solutions are given analytically for this system. This allows us to employ the Melnikov method to detect the chaotic criterion analytically from the breaking of the homoclinic-like and heteroclinic-like orbits in the presence of viscous damping and an external harmonic driving force. The results presented here in this paper show the complicated dynamics for PWLD system of the subharmonic solutions, chaotic solutions and the coexistence of multiple solutions for the single well system, double well system and the triple well dynamics. [ABSTRACT FROM AUTHOR]

In this paper we present a novel formulation of chaotic hybrid inflation in supergravity. The model includes a waterfall field which spontaneously breaks a gauged U 1 ( B – L ) at a GUT scale. This allows for the possibility of future model building which includes the standard formulation of baryogenesis via leptogenesis with the waterfall field decaying into right-handed neutrinos. We have not considered the following issues in this short paper, i.e. supersymmetry breaking, dark matter or the gravitino or moduli problems. Our focus is on showing the compatibility of the present model with Planck, WMAP and Bicep2 data. [ABSTRACT FROM AUTHOR]

In recent years, data hiding has emerged as one of the main research areas in digital security. There are plenty of schemes to hide the secret data into the least significant bit planes of an image. Most of them either traverse the image pixels according to the scanning methods or using some structural fixed patterns. Researchers have proposed data hiding techniques with an orientation of hiding the content of the information, but algorithms are known publicly. Hence, the secret data is prone to be revealed easily. To provide higher security, several methods have been proposed that determine data hiding locations using certain patterns/formula. Chaotic systems have also been effectively utilized to devise secret key based data hiding algorithms. This alleviates the problem of easy retrieval even if the embedding algorithm is known. The present paper proposes a chaotic system based data hiding scheme that provides high payload as well as imperceptibility. In addition, the scheme exhibits excellent performance in terms of data security. [ABSTRACT FROM AUTHOR]

Dynamics of a cluster of chaotic oscillators on a network are studied using coupled maps. By introducing the association schemes, we obtain coupling strength in the adjacency matrices form, which satisfies Markov matrices property. We remark that in general, the stability region of the cluster of oscillators at the synchronization state is characterized by Lyapunov exponent which can be defined based on the N -coupled map. As a detailed physical example, dynamics of microbubble cluster in an ultrasonic field are studied using coupled maps. Microbubble cluster dynamics have an indicative highly active nonlinear phenomenon, were not easy to be explained. In this paper, a cluster of microbubbles with a thin elastic shell based on the modified Keller-Herring equation in an ultrasonic field is demonstrated in the framework of the globally coupled map. On the other hand, a relation between the microbubble elements is replaced by a relation between the vertices. Based on this method, the stability region of microbubbles pulsations at complete synchronization state has been obtained analytically. In this way, distances between microbubbles as coupling strength play the crucial role. In the stability region, we thus observe that the problem of study of dynamics of N -microbubble oscillators reduce to that of a single microbubble. Therefore, the important parameters of the isolated microbubble such as applied pressure, driving frequency and the initial radius have effective behavior on the synchronization state. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic characteristics a three-body tethered satellite system in large elliptic orbits and the control strategy to suppress the libration of the system in orbital transfer process. The system is modeled by a two-piece dumbbell model in the domain of true anomaly. The model consists of one main satellite and two subsatellites connected with two straight, massless and inextensible tethers. Two control strategies based on the sliding mode control are developed to control the libration to the zero state and the steady state respectively. The results of numerical simulations show that the proposed control scheme has good performance in controlling the libration motion of a three-body tethered satellite system in an elliptic orbit with large eccentricity by limited control inputs. Furthermore, Hamiltonians in both states are examined and it shows that less control input is required to control the libration motion to the steady state than that of zero state. [ABSTRACT FROM AUTHOR]

The aim of this paper is to address the codimension-one bifurcation of Marotto’s map and its utility in image encryption. First of all, local stability analysis and local bifurcation analysis of fixed points of the considered map are investigated in details. According to the classical bifurcation theory and the center manifold theorem, the map exhibits various bifurcation types such as transcritical, flip and Neimark–Sacker bifurcations. Second of all, the map is proven to be chaotic in the sense of Marotto. Since image encryption based on chaotic maps is very promising for cryptography, Marotto’s map, compound chaos, and spatiotemporal chaos are combined to encrypt and decrypt images. Numerical simulations agree with the analytical framework for the complex dynamics of the map. Furthermore, different test images are used to demonstrate the effectiveness of the method implemented for encryption. [ABSTRACT FROM AUTHOR]

This paper puts forward the comparative performances for synchronisation between (i) systems from different chaotic system families, (ii) systems from the Unified Chaotic System (UCS) family, (iii) a hyperchaotic and a chaotic systems and (iv) identical chaotic systems. Three different well-known control techniques, i.e. Nonlinear Active Control (NAC), Sliding Mode Control (SMC) and Adaptive Control (AC) are used for synchronisation between various pairs of chaotic and/or hyperchaotic systems. Performances of NAC, SMC and AC techniques are investigated and compared with synchronisation of different pairs of chaotic systems based on the error dynamics and required control inputs. The integral square error and required control energy measures are considered for comparison. Finally, a generalised view on the use of the control techniques for synchronisation is finally proposed. Moreover, a new chaotic system is proposed and its qualitative analysis is done to illustrate the chaotic behaviour of the system. The new system is used as an example of synchronisation. MATLAB simulation results are presented which reflect the successful achievement of the objectives. [ABSTRACT FROM AUTHOR]

In this paper, the bifurcation and chaotic behaviors of a Duffing oscillator with delayed displacement and velocity feedbacks under harmonic excitation are investigated. The analytically necessary condition for the chaos in the sense of Smale horseshoes is established based on Melnikov method. It could be found that the delayed displacement and velocity feedbacks affect the necessary condition respectively, so that the analysis on the effects of the two kinds of feedbacks is presented individually. The effects of displacement feedback coefficient, velocity feedback coefficient and their time delays on the analytically necessary condition are analytically discussed. Furthermore, some typical numerical results, including the bifurcation diagrams, Poincaré maps and the largest Lyapunov exponents of the delayed oscillator are also presented and compared. The satisfactory qualitative agreement between the analytical and numerical results verify the correctness of the analytically necessary condition. [ABSTRACT FROM AUTHOR]

Data encryption of sensor nodes is very important in body area networks (BANs) since the physiological data of an individual are highly sensitive. However, past encryption methods have small key space, which makes them vulnerable to attacks. In this paper, we propose a new encryption algorithm based on combined chaos. Firstly, Logistic and Kent chaotic mappings are introduced to produce two sub-matrices, and then a combined matrix is generated to perform XOR operation with the original data for encryption. The experimental results indicate that the proposed algorithm has a large key space, high key sensitivity and excellent attack resistance ability, and is feasible in privacy protection of BAN system. [ABSTRACT FROM AUTHOR]

Targeted intervention and resource allocation are essential for effective malaria control, particularly in remote areas, with predictive models providing important information for decision making. While a diversity of modeling technique have been used to create predictive models of malaria, no work has made use of Bayesian networks. Bayes nets are attractive due to their ability to represent uncertainty, model time lagged and nonlinear relations, and provide explanations. This paper explores the use of Bayesian networks to model malaria, demonstrating the approach by creating village level models with weekly temporal resolution for Tha Song Yang district in northern Thailand. The networks are learned using data on cases and environmental covariates. Three types of networks are explored: networks for numeric prediction, networks for outbreak prediction, and networks that incorporate spatial autocorrelation. Evaluation of the numeric prediction network shows that the Bayes net has prediction accuracy in terms of mean absolute error of about 1.4 cases for 1 week prediction and 1.7 cases for 6 week prediction. The network for outbreak prediction has an ROC AUC above 0.9 for all prediction horizons. Comparison of prediction accuracy of both Bayes nets against several traditional modeling approaches shows the Bayes nets to outperform the other models for longer time horizon prediction of high incidence transmission. To model spread of malaria over space, we elaborate the models with links between the village networks. This results in some very large models which would be far too laborious to build by hand. So we represent the models as collections of probability logic rules and automatically generate the networks. Evaluation of the models shows that the autocorrelation links significantly improve prediction accuracy for some villages in regions of high incidence. We conclude that spatiotemporal Bayesian networks are a highly promising modeling alternative for prediction of malaria and other vector-borne diseases. [ABSTRACT FROM AUTHOR]

A broad variety of real-world problems have been solved using multilayer perceptron (MLP) artificial neural networks (ANNs). Optimization techniques aid ANNs to select suitable weights and achieve correct results. Recently, the kidney-inspired algorithm (KA) has been proposed for optimization problems. This algorithm is based on the filtration, reabsorption, secretion, and excretion processes that take place in the kidneys of the human body. In the KA, the value of α in the filtration rate formula is a constant value in the range of [0, 1] that is set in the initialization stage of the algorithm. In this paper, an improved KA for optimization of the ANN model is presented in which the filtration rate is controlled by changing the value of α from minimum to maximum during the search process, which helps in achieving a better balance between exploration and exploitation in the algorithm. In this algorithm if more solutes are filtered and moved to filtered blood it means that the algorithm has more exploration. In contrast, if more solutes move to waste it means that more exploitation is performed by the algorithm . In addition, the separate use of three chaotic maps instead of a random number in the movement formula of the modified KA is investigated in order to assess the ability of each map to help to achieve superior results. The proposed method is tested on benchmark classification and time series prediction problems. The method is also applied to a real-world rainfall forecasting problem. The results of a statistical analysis prove the ability of the method. [ABSTRACT FROM AUTHOR]

The success rates of the expert or intelligent systems depend on the selection of the correct data clusters. The k-means algorithm is a well-known method in solving data clustering problems. It suffers not only from a high dependency on the algorithm's initial solution but also from the used distance function. A number of algorithms have been proposed to address the centroid initialization problem, but the produced solution does not produce optimum clusters. This paper proposes three algorithms (i) the search algorithm C-LCA that is an improved League Championship Algorithm (LCA), (ii) a search clustering using C-LCA (SC-LCA), and (iii) a hybrid-clustering algorithm called the hybrid of k-means and Chaotic League Championship Algorithm (KSC-LCA) and this algorithm has of two computation stages. The C-LCA employs chaotic adaptation for the retreat and approach parameters, rather than constants, which can enhance the search capability. Furthermore, to overcome the limitation of the original k-means algorithm using the Euclidean distance that cannot handle the categorical attribute type properly, we adopt the Gower distance and the mechanism for handling a discrete value requirement of the categorical value attribute. The proposed algorithms can handle not only the pure numeric data but also the mixed-type data and can find the best centroids containing categorical values. Experiments were conducted on 14 datasets from the UCI repository. The SC-LCA and KSC-LCA competed with 16 established algorithms including the k-means, k-means++, global k-means algorithms, four search clustering algorithms and nine hybrids of k-means algorithm with several state-of-the-art evolutionary algorithms. The experimental results show that the SC-LCA produces the cluster with the highest F-Measure on the pure categorical dataset and the KSC-LCA produces the cluster with the highest F-Measure for the pure numeric and mixed-type tested datasets. Out of 14 datasets, there were 13 centroids produced by the SC-LCA that had better F-Measures than that of the k-means algorithm. On the Tic-Tac-Toe dataset containing only categorical attributes, the SC-LCA can achieve an F-Measure of 66.61 that is 21.74 points over that of the k-means algorithm (44.87). The KSC-LCA produced better centroids than k-means algorithm in all 14 datasets; the maximum F-Measure improvement was 11.59 points. However, in terms of the computational time, the SC-LCA and KSC-LCA took more NFEs than the k-means and its variants but the KSC-LCA ranks first and SC-LCA ranks fourth among the hybrid clustering and the search clustering algorithms that we tested. Therefore, the SC-LCA and KSC-LCA are general and effective clustering algorithms that could be used when an expert or intelligent system requires an accurate high-speed cluster selection. [ABSTRACT FROM AUTHOR]

Origami is an ancient art of the paper folding that has been the source of inspiration in many engineering designs due to its intrinsic ability of changing shape and volume. Self-expandable devices have been created based on origami concept together with smart materials. Shape memory alloys belong to this class of materials and provide high forces and large displacements by varying their temperature. This work deals with the nonlinear dynamics of an origami-stent, a cylindrical shaped origami structure, which has the capacity of changing its radius. The actuation is provided by antagonistic torsional shape memory alloy wires placed in the origami creases. The mathematical model assumes a polynomial constitutive model to describe the shape memory alloy thermomechanical behavior. Geometric assumptions establish a one-degree of freedom model with constitutive and geometric nonlinearities. Numerical simulations are carried out considering different thermomechanical loadings that represent operational conditions. The system presents complex responses including chaos. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study of two methods to identify and classify intermittent stochastic faults occurring in a dynamic nonlinear chemical process. The methods are based on two popular stochastic modelling techniques, i.e., generalized polynomial chaos expansion (gPC) and Gaussian Process (GP). The goal is to assess which method is more efficient for fault detection and diagnosis (FDD) when using models with parametric uncertainty, and to show the capabilities and drawbacks of each method. The first method is based on a first-principle model combined with a gPC expansion to represent the uncertainty. Resulting statistics such as probability density functions (PDFs) of the measured variables is further used to infer the intermittent faults. For the second method, a GP model is used to project multiple inputs into a univariate model response from which the fault can be identified based on a minimum distance criterion. The performance of the proposed FDD algorithms is illustrated through two examples: (i) a chemical process involving two continuous, stirred tank reactors (CSTRs) and a flash tank separator, and (ii) the Tennessee Eastman benchmark problem. [ABSTRACT FROM AUTHOR]

In the paper, the dynamical behaviors of a new fractional order hyperchaotic Rabinovich system are investigated, which include its local stability, hyperchaos, chaotic control and synchronization. Firstly, a new fractional order hyperchaotic Rabinovich system with Caputo derivative is proposed. Then, the hyperchaotic attractors of the commensurate and incommensurate fractional order hyperchaotic Rabinovich system are found. After that, four linear feedback controllers are designed to stabilize this fractional order system Finally, by using the active control method the synchronization is studied between the fractional order hyperchaotic and chaos controlled Rabinovich system In addition, the theoretical predictions are confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

Global sensitivity analysis (GSA) plays an important role in exploring the respective effects of input variables on response variables. In this paper, a new kernel function derived from orthogonal polynomials is proposed for support vector regression (SVR). Based on this new kernel function, the Sobol’ global sensitivity indices can be computed analytically by the coefficients of the surrogate model built by SVR. In order to improve the performance of the SVR model, a kernel function iteration scheme is introduced further. Due to the excellent generalization performance and structural risk minimization principle, the SVR possesses the advantages of solving non-linear prediction problems with small samples. Thus, the proposed method is capable of computing the Sobol’ indices with a relatively limited number of model evaluations. The proposed method is examined by several examples, and the sensitivity analysis results are compared with the sparse polynomial chaos expansion (PCE), high dimensional model representation (HDMR) and Gaussian radial basis (RBF) SVR model. The examined examples show that the proposed method is an efficient approach for GSA of complex models. [ABSTRACT FROM AUTHOR]

Time delay feedback has been shown to produce chaos from non-chaotic systems. In this paper, besides the single and double scroll chaotic attractors, a new composite multi-scroll attractor is found in stable systems with time delay feedback. From the viewpoint of the local stability analysis, conservation analysis, Lyapunov exponent spectrum and power spectrum, the composite multi-scroll attractor is shown to be a hyper-chaotic attractor. The phase trajectory in the new composite hyper-chaotic multi-scroll attractor diverges in multiple eigen-directions, which improves the security of secure communication and chaotic encryption. A paradigm using the multi-scroll attractor for encryption is proposed, demonstrating its potential applicability. [ABSTRACT FROM AUTHOR]