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In this paper, we study a three-dimensional system of differential equations which is a generalization of the system introduced by Yu and Wang (Eng Technol Appl Sci Res 3:352–358, 2013), a continuation of the study of chaotic attractors [see Yu and Wang (Eng Tech Appl Sci Res 2:209–215, 2012)]. We show that these systems admit a zero-Hopf non-isolated equilibrium point at the origin and prove the existence of a limit cycle emanating from it. We illustrate our results with some numerical simulations. [ABSTRACT FROM AUTHOR]

This paper mainly explores the self-reproducing dynamics in discrete-time system by constructing a two-dimension map with infinitely many fixed points. Theoretical analysis shows that the attractor of the map can not only be non-destructively reproduced by the initial values of all state variables along all axis directions, but can also be non-destructively reproduced by the parameter along all axis directions. The numerical simulations of bifurcation diagram, Lyapunov exponent, phase portrait and iterative sequence are carried out to further confirm the theoretical results. The self-reproducing behavior of different type of attractors and the corresponding iterative sequences are also confirmed by the experimental measurements performed on the DSP-based platform. This map is especially suitable for chaos-based engineering applications since the offset can be periodically switched by the initial condition and parameter on the premise of keeping robust dynamical behavior. [ABSTRACT FROM AUTHOR]

The paper is aimed at mimicking the motion of myriapods by using an array of mechanical arms coupled to an array of FitzHugh–Nagumo (FN) neuron circuits. The differential equation depicting the electromechanical system is achieved by using Kirchhoff's and Newton's laws. The system parameters are sensitive to the stability of the system as shown by numerical simulations such that for different ranges of the stimulation current, the array of the FN neuron circuit coupled to a single mechanical arm is either in the non-excitable state, excitable state or in the oscillatory state. For the values of the stimulation current in the excitable state, an action potential (AP) achieved produced an excitation greater enough to actuate significantly the mechanical leg. In the excitable state, the action of the magnetic signal on the single mechanical arm increases the amplitude of the instantaneous displacement of the legs. The array of the coupled electromechanical system in the excitable state produces an AP for the different values of the legs having the same behavior as shown by numerical simulations, which implied that neurons communicate without loss of amplitude when in the permanent regime. This behavior is similar to the instantaneous displacement of the mechanical legs, hence depicting the straightforward motion of myriapods without rotation. Finally, the velocities of the propagation of nerve impulses and that of the displacement of legs are quantitatively the same. [ABSTRACT FROM AUTHOR]

In recent years, the mathematical model of memristor has attracted extensive attention from researchers, but the boundary effect of the memristor model is rarely considered. A memristor with the window function is proposed in this paper. First, the boundary effect of the device is ignored by the conventional memristive model, but the memristor model with the window function can effectively solve this problem. Then, based on the fractional difference theory, a discrete fractional mathematical model of memristor with the window function is studied. Meanwhile, the corresponding three memristor characteristics are verified for this model in the numerical simulations. Finally, the discrete fractional memristor model is applied to the Logistic map, and we construct a new chaotic map called the discrete fracmemristor Logistic map. The new chaotic sequence is observed. In addition, it provides important mathematical models for many fields, such as chaotic systems, chaotic circuits, and neural networks. [ABSTRACT FROM AUTHOR]

Multistability has been rarely explored in non-autonomous memristive circuit. To involve this issue, a non-autonomous memristive Jerk circuit is proposed to disclose its generation of multistability in this paper. The proposed Jerk circuit contains a memristor with quadratic memductance and an externally applied stimulus. Due to the existence of externally applied stimulus, the circuit has a time-varying equilibrium point with its stability evolving over time. Then, the parameter-related dynamics distribution and bifurcation behaviors are disclosed by multiple numerical tools. It is found that imperfect bifurcation route emerges in the bifurcation diagrams. Then, multistabilities for four representative sets of system parameters near the imperfect bifurcations are explored by the local attraction basin and phase portrait. Afterwards, a PCB-based analog circuit is manually welded and experimental measurements are executed. The experimentally captured coexisting attractors verify the correctness of the numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a hyperchaotic jerk circuit based on cubic memristor is proposed using memristor replacement method and deduces the corresponding dimensionless system. Through the analysis of basic dynamic characteristics, it is found that there are multiple alternating behaviors among period, chaos and hyperchaos, as well as the attractor displacement phenomenon controlled by the offset constant. Then, the multistability of the system is studied in detail, multiple asymmetric coexistence attractors are found, and the symmetric coexistence attractors are analyzed combined with the basin of attraction. Finally, the circuit is designed and simulated, which is consistent with the numerical simulation results. [ABSTRACT FROM AUTHOR]

Numerical simulation of magnetohydrodynamic natural convection heat transfer in a rhombic enclosure of inclination angle 45 ∘ containing copper-water nanofluid has been presented in this paper. The top and bottom walls of the enclosure are subjected to non-uniform heating while left wall being subjected to lower temperature and right wall being maintained adiabatic. The finite element strategy (COMSOL Multiphysics) is used to solve the governing equations. The numerical simulations are done for the parametric values: 10 4 ≤ Rayleigh number ≤ 10 6 ; 0 ≤ Hartmann number ≤ 100; 0 ≤ volume fraction of nanofluid ≤ 0.05. The phase deviation angle (top wall) is varied in the range from 0 to π with amplitude of non linear heating being maintained constant. The motivation of this research goes with the fact that the associated transport phenomenon conveys the implication of designing an optimal thermal system analogous to the theme of non-uniform heating, with the phase angle being a crucial design parameter. The numerical results depict to the fact, that the rate of heat transfer follows non-monotonic trends and is considerably influenced by interplay of the phase shift angle, Rayleigh number and Hartmann number. The results showed that at Rayleigh number ≥ 10 5 , the heat transfer rate gets inhibited by enhancing the magnetic field intensity. The impact of different types of nano particles is illustrated by comparing the results with the results of three different nanofluids, silver– water, titanium dioxide–water and diamond–water nanofluids. [ABSTRACT FROM AUTHOR]

The first section of this paper discusses the stability and Hopf bifurcation for a new dynamical system using stability theory, the center manifold as well as normal form theory. To verify the analytical results, numerical simulations are performed. The second section focuses on controlling the Hopf bifurcation with a robust controller capable of handling a wide range of parameter values. By fine tuning the control parameters, the controller ensures that Hopf bifurcation occurred at P 0 . Furthermore, we postpone the Hopf bifurcation at P + by adjusting the control parameters. [ABSTRACT FROM AUTHOR]

In this paper, the bifurcation and chaotic threshold of Duffing oscillator with fractional-order delayed feedback control is studied. The fractional-order delayed feedback control is equivalent to the approximate integer-order control. It is found that the fractional-order delayed feedback control has the function of displacement feedback and velocity feedback. Then, the analytically necessary condition for generating chaos in Duffing oscillator with fractional-order delayed feedback control is obtained by Melnikov method. The accuracy of the analytically necessary condition by Melnikov method is verified by numerical simulation and the largest Lyapunov exponents of the system. From the analysis of the numerical simulation results, it is found that there are two paths leading to the chaos after period-doubling bifurcations due to different initial values in Duffing oscillator with fractional-order delayed feedback. Finally, the influence of the parameters of the fractional-order delayed feedback control on bifurcation and chaos is analyzed. The increase of the fractional-order delayed feedback gain will resist the generation of chaos. Both time delay and the fractional-order affect the threshold of chaos in the form of trigonometric functions. The better control performance in the system can be obtained by choosing the reasonable fractional order and time delay. Those results present some new system characteristics which provide theoretic guidance to design and control of this kind system. [ABSTRACT FROM AUTHOR]

In this paper, the complex dynamics of a newly proposed 4D hyperchaotic Lorenz-type system are studied. The sufficient conditions of the emergence of periodic solutions and the stability of them at bifurcation points are obtained by averaging theory. The ultimate bound estimation of this hyperchaotic system is derived using the Lyapunov stability theory and the optimization idea, and relevant numerical simulations are given. Finally, a variable-order fractional network of this new 4D hyperchaotic Lorenz-type system is introduced and investigated. [ABSTRACT FROM AUTHOR]

In this paper, a model of active control system with state-dependent actuation time delay is investigated. Galerkin projection scheme is used to obtain its low dimensional approximation system. State-dependency and effect on dynamics and performance of actuation delay in this active control system are considered. The following results are obtained. Firstly, a state-dependent actuation delay is proposed, which has never been reported in the previous works. It displays that actuation delay is state-dependent. Secondly, employing Galerkin projection scheme, low dimensional approximation system of this delayed active control system is obtained. At last, its stability and Hopf bifurcation are investigated by Routh-Hurwitz Criterion and Hopf bifurcation theory. Using software WinPP, numerical simulation is executed and supports the theoretical results in this paper. [ABSTRACT FROM AUTHOR]

This paper studies one dimensional bubbly cavitating flow of elastic fluids through micro sized nozzles of different shapes. Cavitating flows are applicable in wide range of applications in medical and engineering sciences, such as, the cleansing of teeth, ultrasound and cancer treatment. They are also responsible for erosion on metallic surfaces, damages to machinery, pumps etc. The above make advances in the field important and useful in reducing possible destructive effects of such flows. In current study two types of elastic fluid models namely neo-Hookean and linear elastic are considered. The nonlinear dynamics of bubbly mixture is modeled by incorporating the Rayleigh–Plesset equation. The system is modelled by nonlinear system of ordinary differential equations, which are reduced to non-dimensional form via suitable similarity transformations. The Runge–Kutta numerical technique of 4th order is utilized to solve the set of flow equations. The influences of various emerging parameters on bubble radius, velocity profile and pressure of bubble are illustrated graphically and discussed in detail. [ABSTRACT FROM AUTHOR]

This paper puts forward the control of chaos in the biological system. A new controller based on recursive backstepping sliding mode control is proposed such that it can control the chaotic dynamics in the biological system to stabilize at any position or to track any trajectory that is a smooth function of time. A proportional integral switching surface is proposed to achieve the stability condition of the error dynamics. Unlike the open loop and open plus closed loop control techniques, the design of proposed controller does not require the parameter perturbation. The required stability condition is derived based on Lyapunov stability theory. Simulation is achieved in MATLAB environment. Numerical simulation results are presented in order to show the effective verification of the proposed controller design. Simulation results correspond that the objective of chaos control is achieved successfully. [ABSTRACT FROM AUTHOR]

This paper reports a unified asymmetric memristive diode-bridge (UAMD) emulator with the current constraints for each pair of parallel bridge arms, which is implemented by an asymmetric diode-bridge cascaded with a parallel resistor and capacitor (RC) filter. The mathematical model is established and its pinched property is confirmed by multisim circuit analysis, MATLAB numerical simulation and hardware experiment. Besides, the UAMD emulator is expanded to the general cases and four diodes on symmetric bridge arms owning two situations are taken as two expanding examples. [ABSTRACT FROM AUTHOR]

The operation of memristive, meminductive and memcapacitive circuit components depend on their history of devices, i.e. they are memory dependent. This paper proposes new fractional-order (FO) models of four such circuits since FO derivative is calculated using the past history of time and helps in understanding the memory-dependent dynamics of these memory devices better as compared to the integral derivative. Interestingly, these fractional-order memristive, meminductive and memcapacitive systems (FOMMMSs) display a myriad of dynamics such as ranging from coexisting to hidden attractors, chaotic to hyperchaotic attractors, periodic orbits to stable foci, bursting oscillations transitioning from chaos to periodic states and vice versa, offset boosting phenomenon, and a varied nature of infinite equilibria. The proposed fractional-order systems can have a number of applications such as in oscillator circuits, and secure communication due to the increased randomness of hidden multistability. The theoretical analyses of existence of multistability and hidden attractors in the proposed FOMMMSs comply with that of the numerical simulation and circuit implementation results. [ABSTRACT FROM AUTHOR]

In this contribution, we perform a detailed study of the effect of electromagnetic induction on the dynamical behavior of laser diode modeled by novel single-mode four-dimensional rate equations. Memristor is used to describe electromagnetic induction effect. As result, the obtained model is equilibrium free thus displays hidden dynamics. Consequently, Shilnikov method is not suitable to explain the chaos mechanism in the introduced laser model. Furthermore, there is no heteroclinic nor homoclinic orbit. Based on numerical simulations, we found that the laser model displays hidden dynamics including period doubling bifurcation, multistability (with three different stable states) and crisis phenomena when the electromagnetic strength is varied. The circuit emulator of laser model investigated in this paper has been designed in the Pspice environment to further support numerical results. [ABSTRACT FROM AUTHOR]

In this paper, we have analysed a binary chemical nanofluid dissipative flow (in two cases i.e., 50% EG + 50% water/silica and 50% EG + 50% water/graphene oxide) due to a curved stretching sheet with activation energy. Appropriate transformations yield the nonlinear ordinary differential system. Shooting procedure (R-K 4th order based) is executed to solve the resultant equations. Graphical illustrations thoroughly demonstrate the features of the involved pertinent parameters. We have deliberated the behaviour of the alike parameters on the rate of transfers (heat and mass) and surface drag force (skin friction coefficient) by means of tables. This investigation reveals that (a) reaction rate parameter and temperature difference parameter are helpful to ameliorate the mass transfer rate (b) concentration enhances for higher estimation of activation energy variable (c) increasing the volume fraction of nanoparticles reflects an escalation in temperature (d) heat transfer rate enhancement is recognized for the influence of heat transfer Biot number. At the end this study, we came to know that the EG-Water + Graphene Oxide mixture has more heat transfer rate compared to EG-Water + Silica mixture. This outcome helps to conclude that, whenever the more heat transport required in manufacturing and industries, we can take the EG-Water + Graphene Oxide mixture. [ABSTRACT FROM AUTHOR]

The dynamics of indirect field oriented control (IFOC) of 3-phase induction motor is studied in this paper. The dynamical behaviors of the studied system are performed using bifurcation diagrams, maximum Lyapunov exponent plots, phase portraits, and isospike diagram. The numerical simulation results reveal that the IFOC of 3-phase induction motor displays coexistence of attractors for the same set of IFOC of 3-phase induction motor parameters, periodic and chaotic bursting oscillations. Basins of attraction of different competing attractors are plotted showing complex basin boundaries. The numerical simulation finding are validated by the OrCAD-Spice results. [ABSTRACT FROM AUTHOR]

A new three-dimensional continuous autonomous system is proposed in this paper and it exhibits single scroll chaotic behavior in a particular parameter region. By linear stability analysis and numerical simulations, we investigate different dynamical observations with respect to system parameters and try to understand the route to generation of chaos. For a large portion of the parameter region, we see a sudden birth of a period-three limit cycle. Then the period-three orbit turns into a chaotic state through typical Pomeau-Manneville intermittent route to chaos. Lyapunov exponent and Kaplan-Yorke dimension are used to verify the chaotic behavior. It becomes periodic via inverse period-doubling route for higher values of the parameters. A two-parameter bifurcation diagram is shown which distinguishes the chaotic region from other periodic and steady-state regions. [ABSTRACT FROM AUTHOR]

This paper generalizes a second-order-memristor-based jerk circuit, which is achieved by substituting the first-order memristor contained diode-bridge and RC filter in an existing memristive jerk circuit with a second-order one composed of diode-bridge and LC network. The second-order-memristor-based jerk circuit possesses an unstable saddle-focus and generates complex parameter-dependent dynamics, including hyperchaos, chaos, quasi-period, and period along with coexisting behaviors. The coexistences of symmetric chaotic and quasi-periodic attractors are shown by local attraction basins. Particularly, 2D two-layer-based dynamical maps on the system parameter spaces are employed to perfectly detect complex dynamical behaviors of hyperchaos and quasi-period. Furthermore, hardware breadboard is made for experimental investigations and the measurement results well validate complex parameter-dependent dynamics revealed by the numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a memristor-based chaotic circuit is built by replacing the nonlinear resistor of a unified Van der Pol-Duffing circuit by an ideal and active flux-controlled memristor with an absolute value nonlinearity. The equilibrium points of the mathematical model describing the proposed absolute memristor Van der Pol-Duffing circuit are determined and their stabilities are analyzed thank to the Routh-Hurwitz criteria. The numerical simulations reveal that the proposed absolute memristor circuit exhibits reverse period-doubling to chaos, bistable one-scroll chaotic attractors, double-scroll chaotic attractor, bistable periodic attractors and antimonotonicity phenomenon. Moreover the proposed absolute memristor circuit is implemented in PSIM software package. The results found using the PSIM software package have a good qualitative agreement with those found during the numerical simulations. [ABSTRACT FROM AUTHOR]

This article analyzes a fractional-order SEIR infection epidemic model, including time delays and vaccination strategies. Four differential equations describe the infection dynamics with non-integer derivative orders, which account for memory effects and non-local interactions in disease spread. The paper first establishes the existence and uniqueness of the solution and presents equilibrium points based on the basic reproduction number, R0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R_{0}$$\end{document}. Using the Lyapunov direct method, the global stability of each equilibrium is proven to depend primarily on R0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R_{0}$$\end{document}. Theoretical findings are validated through numerical simulations, exploring the impact of vaccination and fractional derivatives on the epidemic dynamics. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics of kidnapping incidents through the application of the Lotka-Volterra model with fractional order modeling. Drawing parallels between predator–prey interactions in ecological systems and the relationship between Kidnappers and Victims, this study aims to provide insights into the complex phenomenon of kidnapping. Theoretical foundations are established through key definitions and theorems, paving the way for the construction of the model. The existence and uniqueness of solutions to the model equations are examined, followed by a stability analysis to assess the long-term dynamics of kidnapping incidents. Numerical simulations are conducted to validate the theoretical framework and explore the sensitivity of the model to different parameters and initial conditions. By employing the Lotka-Volterra model with fractional order modeling, the study gives a deeper understanding of kidnapping incidents by drawing parallels with ecological systems, allowing for a more comprehensive analysis of the complex interactions between perpetrators and victims. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a fractional-order microscopic chaotic system, derived from a set of microscopic chemical reactions. The dynamical properties of the proposed model have been investigated through Lyapunov characteristic exponents, bifurcation, spectral entropy and C0 complexity algorithm. The results show that the system has rich dynamics in derivative order and the system parameter. In addition, multiple coexisting attractors are found in the system by selecting appropriate initial values. Complexity measuring algorithms are developed as an effective tool for the detection of such attractors. The results are effective for the dynamical randomness in the collisional motion of atoms and molecules in fluids to produce the deterministic chemical chaos, even in fractional order. [ABSTRACT FROM AUTHOR]

The present study investigates the dynamical properties of a fractional order coronary artery system and its control with uncertainties in the parameters. The fractional order model of the coronary artery system (FOCA) is derived using the Grünwald-Letnikov method and the properties of the FOCA system are discussed. Bifurcation plots of the system in the parameter space are derived and presented. The novelty of the paper is the identification of the multistable feature shown by the FOCA system, which has not been discussed in the research literature. Various coexisting attractors are also presented to show the multistability. An adaptive sliding mode controller is designed to stabilize the chaotic oscillations in the FOCA system. Numerical simulations are conducted to indicate the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

In this paper, the stationary probability distribution (SPD) function and the mean first passage time (MFPT) are investigated in a tumor growth model driven by non-Gaussian noise which is introduced to mimic random fluctuations in the levels of the immune system. Results demonstrate the different transitions induced by the strength of non-Gaussian noise under different immune coefficients and the dual roles of non-Gaussian noise in promoting host protection against cancer and in facilitating tumor escape from immune destruction. Additionally, it can be discovered that increases in noise strength, the degree of departure from Gaussian noise, and the immune coefficient can accelerate the extinction of tumor cells. Numerical simulations are performed, and their results present good agreement with the theoretical results. [ABSTRACT FROM AUTHOR]

At present, researchers only find that memristor-based time-delay (MBTD) chaotic systems have rich dynamic behaviors. However, there are still many difficulties in the analysis and application of the MBTD chaotic system. Therefore, a novel 3-D MBTD chaotic system with extreme multi-stability and line equilibrium points is proposed in this work. First, by applying dynamic analysis and numerical simulation, basic behaviors of the system are employed to illustrate the superiority of the system. Then, some special nonlinear phenomena are observed by two-parameter bifurcation diagrams, such as coexisting hidden attractors of both periodic and chaotic, coexisting multi-scroll hidden attractors, coexisting single-scroll hidden attractors and coexisting periodic attractors, which mean that hidden extreme multi-stability occurs. Moreover, the system which has good autocorrelation and cross-correlation is applied to generate the chaotic pseudo-random sequence. Finally, the approximate entropy of the chaotic pseudo-random sequence is larger than that of other time-delay chaotic systems. The above manifest that this MBTD chaotic system possesses abundant dynamics and good randomness. Hence this system owns latent force in the application of memristor. [ABSTRACT FROM AUTHOR]

The aim of the paper is to propose an algorithm based on the Multispin Coding technique for the Kob-Andersen glassy dynamics. We first give motivations to speed up the numerical simulation in the context of spin glass models [M. Mezard, G. Parisi, M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987)]; after defining the Markovian dynamics as in [W. Kob, H.C. Andersen, Phys. Rev. E 48, 4364 (1993)] as well as the related interesting observables, we extend it to the more general framework of random regular graphs, listing at the same time some known analytical results [C. Toninelli, G. Biroli, D.S. Fisher, J. Stat. Phys. 120, 167 (2005)]. The purpose of this work is a dual one; firstly, we describe how bitwise operators can be used to build up the algorithm by carefully exploiting the way data are stored on a computer. Since it was first introduced [M. Creutz, L. Jacobs, C. Rebbi, Phys. Rev. D 20, 1915 (1979); C. Rebbi, R.H. Swendsen, Phys. Rev. D 21, 4094 (1980)], this technique has been widely used to perform Monte Carlo simulations for Ising and Potts spin systems; however, it can be successfully adapted to more complex systems in which microscopic parameters may assume boolean values. Secondly, we introduce a random graph in which a characteristic parameter allows to tune the possible transition point. A consistent part is devoted to listing the numerical results obtained by running numerical simulations. [ABSTRACT FROM AUTHOR]

The memory effect has seen a surge of research into its fundamental properties and applications since its discovery by Feng et al. [Phys. Rev. Lett. 61, 834 (1988)]. While the wave trajectories for which the memory effect holds are hidden implicitly in the diffusion probability function [Phys. Rev. B 40, 737 (1989)], the physical intuition of why these trajectories satisfy the memory effect has often been masked by the derivation of the memory correlation function itself. In this paper, we explicitly derive the specific trajectories through a random medium for which the memory effect holds. Our approach shows that the memory effect follows from a simple conservation argument, which imposes geometrical constraints on the random trajectories that contribute to the memory effect. We illustrate the time-domain effects of these geometrical constraints with numerical simulations of pulse transmission through a random medium. The results of our derivation and numerical simulations are consistent with established theory and experimentation. [ABSTRACT FROM AUTHOR]

Based on the original stretch-twist-fold flow, we propose a unified stretch–twist–fold (USTF) flow. We explore the conditions that zero-Hopf bifurcation occurs at the origin. Using the first-order averaging theorem, a periodic solution produced from the zero-Hopf equilibrium is derived. In addition, we obtain the conclusion that for parameter α large enough, the periodic orbit of USTF flow exists as well unstable. Finally, circuit design has been built for implementing the new system, showing a good agreement between computer simulations and experimental observations. [ABSTRACT FROM AUTHOR]

The dynamics of the ring of unidirectionally coupled single-well Duffing oscillators is analyzed in numerical simulation for identical nodal oscillators. The research is concentrated on the existence of the stable 3D torus attractor in this system. It is shown that 3-frequency quasi-periodicity can be robustly stable in wide range of parameters of the system under consideration. As an explanation of this stability, the conjecture on the coexistence and superposition of two independent effects characterized with irrational frequencies, i.e., the classical Newhouse, Ruelle and Takens scenario and rotating wave flow, is formulated. [ABSTRACT FROM AUTHOR]

In this paper, a fourth-order hyperchaotic circuit with smooth diode-based nonlinearity is modified from the Tamaševičius oscillator. The hyperchaotic circuit has both simple topology and algebraic equation. Some previously uncovered dynamical behaviours of multiple coexisting bifurcations, bi-stability, and offset boosting are revealed by theoretical analyses and numerical simulations. These findings are further verified by circuit simulations and hardware experiments. [ABSTRACT FROM AUTHOR]

In this paper, an autonomous RC hyperjerk like-chaotic circuit with cubic nonlinearity is introduced and investigated. The state equations of the proposed hyperjerk chaotic circuit are described using Kirchhoff's laws. Some fundamental properties of the system such as symmetry, dissipation, equilibrium points and stability are examined. It is found that the system has three equilibrium points which are all unstable. By varying the parameters of the system, it is revealed from numerical simulations that the system exhibits some interesting dynamics including crisis event, hysteretic dynamics (inducing the coexistence of attractors) and transient chaos. To the best of the authors' knowledge, the results of this work represent the first report on the phenomenon of transient chaos in a hyperjerk like-chaotic system and thus deserve dissemination. Hardware experiments are performed to support numerical simulations. The results from hardware experiments are in good agreement with numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, an integer- and fractional-order form of a four-dimensional (4-D) chaotic system with hidden attractors is investigated using theoretical/numerical and analogue methods. The system is constructed not through the extension of a three-dimensional existing nonlinear system as in current approaches, but by modifying the well-known two-dimensional Lotka-Volterra system. The equilibrium point of the integer-order system is determined and its stability analysis is studied using Routh-Hurwitz criterion. When the selected bifurcation parameter is varied, the system exhibits various dynamical behaviors and features including intermittency route to chaos, chaotic bursting oscillations and offset boosting. Moreover, the fractional-order form of the system is examined through bifurcation analysis. It is revealed that chaotic behaviors still exist in the system with order less than four. To validate the numerical approaches, a corresponding electronic circuit for the model in its integer and fractional order form is designed and implemented in Orcard-Pspice software. The Pspice results are consistent with those from the numerical simulations. [ABSTRACT FROM AUTHOR]

A mathematical model of selective laser melting (SLM) of fine-grained metallic powders under the pulse laser annealing conditions has been developed. The processed powder bed is considered in the approximation of continuous medium where its effective thermophysical properties depend on local porosity. The model allows simulation of unsteady distributions of temperature, specific enthalpy, local porosity, morphology and thickness of the processed track. In the paper, all stages of problem analysis are described including its mathematical formulation and numerical implementation. To take into account shrinkage of the powder layer during sintering and remelting, the numerical model utilizes the arbitrary Lagrangian–Eulerian (ALE) method. Thus the finite element mesh provides robust control of quality and dynamic remeshing through adaptive mesh refinement. Using the proposed numerical model the unsteady thermal fields and local porosity of a Fe-based powder layer processed with a pulsed laser has been investigated. [ABSTRACT FROM AUTHOR]

This paper investigates twin attractors in a two-neuron-based non-autonomous Hopfield neural network (HNN) through numerical analyses and hardware experiments. Stability analysis of the DC equilibrium point is executed and an unstable saddle-focus is found in the parameter region of interest. The stimulus-associated dynamical behaviors are numerically explored by bifurcation diagrams and dynamical map in two-dimensional parameter-space, from which coexisting twin attractors behavior can be observed with the variations of two stimulus-associated parameters. Moreover, breadboard experiment investigations are carried out, which effectively verify the numerical simulations. [ABSTRACT FROM AUTHOR]

The kinetics of phase ordering has been investigated for numerous systems via the growth of the characteristic length scale ℓ (t) ∼ t α quantifying the size of ordered domains as a function of time t, where α is the growth exponent. The behavior of the squared magnetization ⟨ m (t) 2 ⟩ has mostly been ignored, even though it is one of the most fundamental observables for spin systems. This is most likely due to its vanishing for quenches in the thermodynamic limit. For finite systems, on the other hand, we show that the squared magnetization does not vanish and may be used as an easier to extract alternative to the characteristic length. In particular, using analytical arguments and numerical simulations, we show that for quenches into the ordered phase, one finds ⟨ m (t) 2 ⟩ ∼ m 0 2 t d α / V , where m 0 is the equilibrium magnetization, d the spatial dimension, and V the volume of the system. [ABSTRACT FROM AUTHOR]

This study, the effect of constitutional supercooling appearing ahead of the crystallization front and leading to the mushy layer origination is considered. An approximate analytical theory determining the time of mushy layer initiation is constructed. Theoretical predictions are in good agreement with numerical simulations carried out in previous studies. [ABSTRACT FROM AUTHOR]

The framework of this paper is to investigate the mitigation ability of an expanded rigid polyurethane foam against extremely fast (>106 s−1) and intense ( >10 GPa) dynamic loadings. Cyclic quasi-static tests and dynamic experiments (gas gun and low inductance generator) have been performed to investigate the foam behaviour for strain rates ranging from 10−3 to 105 s−1. Analysis of the experimental results shows that the foam has an elastic behaviour phase followed by a compaction phase with significant permanent sets. Compaction threshold is about 8 MPa under quasi-static loading, and 21 MPa for strain rates above 104 s−1. A porous compaction model is used to represent the macroscopic behaviour of the foam for the whole range of strain rates. The parameters are identified from dynamic experimental results. The model is validated by comparing calculated velocity profiles with an explicit hydrocode and velocity profiles measured during the experiments. [ABSTRACT FROM AUTHOR]

The paper has considered the fractal flow in a dual media with fractal properties, where the media could be elastic, heterogeneous and visco-elastic. We argued that, the fractal flow within a geological formation with elastic property cannot be accurately described with the concept of differentiation with local operator, as this operator is unable to include into mathematical formulation the effect of elasticity. Thus to include into mathematical formula the observed facts, we have modified the model by replacing the local derivative with the non-local operator with power. A more complex problem was considered where the geological formation is considered to have visco-elastic and heterogeneity properties. We argued that, the flow within a matrix rock with these two properties cannot either be described with local derivative nor a non-local derivative with power law. In this case two non-local operators were considered, an operator with Mittag-Leffler kernel and Mittag-Leffler-Power law kernel [F. Ali et al., J. Magn. Magn. Mater. 423, 327 (2017); F. Ali et al., Eur. Phys. J. Plus 131, 310 (2016); F. Ali et al., Eur. Phys. J. Plus 131, 377 (2016); F. Ali et al., Nonlinear Sci. Lett. A 8, 101 (2017); N.A. Sheikh et al., Neural Comput. Appl. (2016) https://doi.org/10.1007/s00521-016-2815-5]. For each model, a detailed study of existence and uniqueness of the system solutions was presented using the fixed point theorem. We solved numerically each model using a more acculturate numerical scheme known as Upwind. Some numerical simulations are presented to underpin the effect of the suggested fractional differentiation. [ABSTRACT FROM AUTHOR]

We explore the capabilities of multiresolution wavelet analysis (MWA) to characterize complex dynamics based on short data sets that can be applied for diagnosing inter-state transitions. Using the example of chaos–hyperchaos transitions in the model of two interacting Rössler systems, we establish the minimum amount of data necessary for reliable separation of chaotic and hyperchaotic oscillations and discuss how this amount changes depending on the length of the transient process. We then discuss transitions between wakefulness and artificial sleep in mice and estimate the duration of electroencephalograms (EEG) that provide separation between these states. [ABSTRACT FROM AUTHOR]

When the bursting electrical activity (BEA) of the β -cells inside Langerhans' islet behave synchronously, the insulin secretes into the bloodstream to regulate the body's glucose levels. Recent advances in pancreas imaging techniques showed that the communication path among β -cells exhibits a small-world-like organization. Hence, we propose a mathematical model of a cluster composed of β -cells with different BEAs represented by a complex network of nearly identical nodes. Each node describes the dynamics of an isolated β -cell by the Pernarowski model. We analyze the effect of shortest path communication on the synchronization of β -cells with different types of BEA via numerical simulations and electronic circuit experiments. Our results showed that even when the BEA evolves to distinct dynamics among the nodes, the synchronization is achieved. Of particular interest is when a percentage of β -cells (nodes) are silent, i.e., no BEA is generated, which is a typical condition associated with diabetes. In this scenario, we observed that the proposed model predicts that the interaction between silent and active β -cells induces reactivation of the inactive β -cells' electrical activity. [ABSTRACT FROM AUTHOR]

In this work, we study the synchronization states for a specific pair of mutually coupled multistable scroll systems. First, we determine conditions in the coupling scheme, to achieve partial or complete synchronization, under a uniform-coupling strength. Second, it is analyzed how the changes in the coupling strength modify the synchronous state. Our main results show that the nature of the coupling scheme determines the obtained synchronization type, while the coupling strength allows us to have various synchronized state attractors that differ from initial attractors. The analysis of the emergence of stable collective behavior is presented using Lyapunov functions of the different couplings and illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

The effect of the Soret and Dufour parameters on the peristaltic transport of a magneto six-constant Jeffreys nanofluids in a non-uniform channel are examined in this research. The mathematical modeling of six-constant Jeffreys nanofluids with double-diffusivity convection and inclined magnetic field is provided with a detailed description. To simplify partial differential equations that are highly nonlinear in nature, the long wavelength and low approximation of the Reynolds number are used. The reduced differential equations are solved by numerical method. The exact temperature, concentration and nanoparticle solutions are calculated. The importance of the various physical parameters of flow quantities is shown in numerical and graphical data. It is observed that the nanosolid particle concentration drops when large values of Brownian motion parameter and Soret number are considered. Furthermore, random collusions transfer molecular kinetic energy into thermal energy during the micro-mixing process of solid nanoparticles within the nanoliquid, resulting in a rise in fluid temperature. [ABSTRACT FROM AUTHOR]

We introduce statistical techniques required to handle complex computer models with potential applications to astronomy. Computer experiments play a critical role in almost all fields of scientific research and engineering. These computer experiments, or simulators, are often computationally expensive, leading to the use of emulators for rapidly approximating the outcome of the experiment. Gaussian process models, also known as Kriging, are the most common choice of emulator. While emulators offer significant improvements in computation over computer simulators, they require a selection of inputs along with the corresponding outputs of the computer experiment to function well. Thus, it is important to select inputs judiciously for the full computer simulation to construct an accurate emulator. Space-filling designs are efficient when the general response surface of the outcome is unknown, and thus they are a popular choice when selecting simulator inputs for building an emulator. In this tutorial we discuss how to construct these space filling designs, perform the subsequent fitting of the Gaussian process surrogates, and briefly indicate their potential applications to astronomy research. [ABSTRACT FROM AUTHOR]

In this study, the ferroresonant modes are investigated by depending on core losses and the problem of chaotic motion on a ferroresonant circuit is considered. We study the problem of control of chaos in ferroresonant circuit using backstepping nonlinear control to become stable in the equilibrium point and converge to desired trajectory or point. A recursive backstepping control theory is utilized to design an appropriate control input signal which achieve the control of the system based on Lyapunov theory. For the comparison, the control of chaos in ferroresonant condition with one and two control inputs designed using backstepping theory is compared. Numerical simulations are used to demonstrate the effectiveness of designed control inputs for chaos control in ferroresonant phenomena. [ABSTRACT FROM AUTHOR]

A sealed annular geometry containing nanoliquids with differently heated boundaries aptly describes the geometrical structure of many important cooling applications. The present study reports the numerical investigation on the effect of axially varying temperature in the form of sinusoidal thermal profiles along the side walls of an annular enclosure containing different hybrid nanoliquids with insulated horizontal boundaries. An implicit FDM based approach is adopted to solve the transient and steady-state model equations and numerical simulations are presented to describe the qualitative flow behavior as well as the quantitative thermal transport rates. The prime objective of the analysis is to enhance the buoyant flow circulation strength as well as the associated thermal dissipation rates and is achieved by identifying a suitable combination of nanoparticle along with a proper choice of geometrical parameters. Numerical predictions revealed the buoyant motion and thermal dissipation rate could be effectively controlled by a proper selection of phase deviation. Further, the appropriate combination of nanoparticles is another crucial parameter in enhancing the thermal transport in the geometry. [ABSTRACT FROM AUTHOR]

The model of a non-autonomous memristor-based oscillator with a line of equilibria is studied. A numerical simulation of the system driven by a periodic force is combined with a theoretical analysis by means of the quasi-harmonic reduction. Both two mechanisms of synchronization are demonstrated: phase and frequency locking and suppression by an external signal. Classification of undamped oscillations in an autonomous system with a line of equilibria as a special kind of self-sustained oscillations is concluded due to the possibility to observe the effect of frequency-phase locking in the same system in the presence of an external influence. It is established that the occurrence of phase locking in the considered system continuously depends both on parameter values and initial conditions. The simultaneous dependence of synchronization area boundaries on the initial conditions and the parameter values is also shown. [ABSTRACT FROM AUTHOR]

We hereby propose a cosine chaotification technique (CCT), which has simple structure, complex nonlinear dynamics and bounded orbits, to enhance the chaotic behavior as well as the complexity performance of discrete chaotic systems. To demonstrate the effectiveness of the CCT, we apply the CCT on three different examples, including one-dimensional (1D) logistic map, two population chaotic maps, and the three-dimensional (3D) Hénon map. Performance evaluations prove that the CCT can change the chaotic and non-chaotic states of these maps to chaotic or hyperchaotic state with higher complexity performance. Besides that, the generated maps by CCT have wider chaotic and hyperchaotic behaviors than the existing chaotic maps. [ABSTRACT FROM AUTHOR]

One of the most basic ingredients of fractal or multifractal is its scale-invariance or self-similar property albeit they appear seemingly disordered or apparently bewildering. In this article, we give several examples of deterministic, random and stochastic fractals as well as multifractals to show that there is always at least one conservation law behind all these systems. On the other hand, it is well-known and it has been shown here too that fractals and multifractals are self-similar which is also some form of symmetry that sends the object to itself. This is reminiscent to Noether's first theorem that states that for every continuous symmetry of an action, there exists a conserved quantity. Finding the connection between conserved quantity in fractal and multifractal with scale-invariance of self-similarity can actually be coined as an equivalent counterpart of the Noether's first theorem. [ABSTRACT FROM AUTHOR]