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In this paper, the fractional space-time nonlinear Chen-Lee-Liu equation has been considered using various methods. The investigation of the transition from periodic to quasi-periodic behavior has been conducted using a saddle-node bifurcation approach. The paper reports the conditions of multi-dimensional bifurcations of dynamical solutions. Additionally, a direct algebraic method has been used to calculate various 2D and 3D solitonic structures of the equation, and an analysis of their accuracy and effectiveness has been conducted. Furthermore, the Galilean transformation has been used to convert the equation into a planar dynamical system, which is further utilized to obtain bifurcations and chaotic structures. Chaotic structures of perturbed dynamical system are observed and detected through chaos detecting tools such as 2D-phase portrait, 3D-phase portrait, time series analysis, multistability and Lyapunov exponents over time. Further, sensitivity behavior for a range of initial conditions, both perturbed and unperturbed. The results suggest that the investigated equation exhibits a higher degree of multi-stability. [ABSTRACT FROM AUTHOR]

The existence of time delay in complex industrial processes or dynamical systems is a common phenomenon and is a difficult problem to deal with in industrial control systems, as well as in the textile field. Accurate identification of the time delay can greatly improve the efficiency of the design of industrial process control systems. The time delay identification methods based on mathematical modeling require prior knowledge of the structural information of the model, especially for nonlinear systems. The neural network-based identification method can predict the time delay of the system, but cannot accurately obtain the specific parameters of the time delay. Benefit from the interpretability of machine learning, a novel method for delay identification based on an interpretable regression decision tree is proposed. Utilizing the self-explanatory analysis of the decision tree model, the parameters with the highest feature importance are obtained to identify the time delay of the system. Excellent results are gained by the simulation data of linear and nonlinear control systems, and the time delay of the systems can be accurately identified. [ABSTRACT FROM AUTHOR]

A novel three-dimensional Clef chaotic attractor system is proposed in this paper and the consistent occurring dynamical behaviors of the attractor is analyzed and the subsequent Lyapunov exponents, Poincare´ maps etc., are computed accordingly. The attractor is named Clef as it resembles the shape of the musical notation Clef. Quest on dynamical systems has led the researchers to invent various dynamical systems and strange attractors solving conservative applications in engineering science. Principally in shielding the superabundant multimedia content for data encryption and compression imposing greater complexity to the crypto systems and also strange attractors outperforms in the material science field for instance identifying the metal corrosion, controlling vibroformers, controlling turbulence etc., supplementary to the above, chaos expands its rays of hope and lucrative in economics, stock market, psychology and much more scientific fields. [ABSTRACT FROM AUTHOR]

Across different domains, there are 'star performers' who are able to generate disproportionate levels of performance output. To date, little is known about the model principles underlying the rise of star performers. Here, we propose that star performers' abilities develop according to a multi-dimensional, multiplicative and dynamical process. Based on existing literature, we defined a dynamic network model, including different parameters functioning as enhancers or inhibitors of star performance. The enhancers were multiplicity of productivity, monopolistic productivity, job autonomy, and job complexity, whereas productivity ceiling was an inhibitor. These enhancers and inhibitors were expected to influence the tail-heaviness of the performance distribution. We therefore simulated several samples of performers, thereby including the assumed enhancers and inhibitors in the dynamic networks and compared their tailheaviness. Results showed that the dynamic network model resulted in heavier and lighter tail distributions, when including the enhancer- and inhibitorparameters, respectively. Together, these results provide novel insights into the dynamical principles that give rise to star performers in the population. [ABSTRACT FROM AUTHOR]

The momentum method has become the workhorse in the deep learning community. To theoretical understand its success, researchers put efforts in demystifying its convergence properties when optimizing neural networks. For the convex problem, it is well-known that the triple momentum (TM) method owns the fastest theoretical convergence rate among all first-order methods. However, there exists no theoretical convergence results about the TM method in solving the non-convex neural networks training problem, let alone its acceleration guarantee. In this paper, we focus on the training process of the TM method for a two-layer ReLU neural network. Inspired by the accurate characterization of the high-resolution dynamical system, we consider the high-resolution ordinary differential equation (ODE) of the TM method. Under the over-parameterized assumption, we derive that the original non-convex optimization problem can be transformed to a strongly convex task. By applying an appropriate Lyapunov function, we prove that the TM method can linearly converge to a global minimum. Compared to the heavy ball method and Nesterov's accelerated gradient method, our result provides the first guarantee for the acceleration of the TM method in training neural networks. Through empirical experiments, the accelerated convergence of the TM method and the effect of over-parameterization are validated. [ABSTRACT FROM AUTHOR]

Poincaré surface of section is an important tool in the dynamical system which allow us to imagine and understand the numerical solution behavior of the system. Hide's couple dynamo model is rich and worth to study. In this paper, we apply the Poincaré surface of section in three cases periodic orbit motion, regular motion and chaos motion. [ABSTRACT FROM AUTHOR]

The Ebola virus disease (EVD) is one of the deadly diseases amongst human and non-human primates caused by most virulent pathogens Ebola virus. Socio-economic impacts of Ebola is very high. In 2014, the latest and largest major outbreak occurred in West African countries Guinea, Sierra Leone, and Liberia. During the outbreak, cases were reported about presence of Ebola virus in semen and breast milk of individuals after recovery. Vertical transmission of disease spread and its impacts on population are studied in this research. How effectively early diagnosis, isolation, awareness campaigns break the chain of infectious cases and control disease spread is studied. Mathematical model for vertical transmission of Ebola with media effect is developed using seven compartments namely susceptible, exposed, infectious, Hospitalised/Isolated, Convalescent, Dead (not properly buried dead bodies of Ebola victims), and Recovered. Basic reproduction number, Disease free equilibrium, Endemic equilibrium are derived. Stability of DFE and EE is established. Numerical simulations are carried out. It is observed that mass media is one of the most effective ways of creating awareness about such type of high mortality disease. Informative awareness amongst public may curb the disease spread and help to control disease in initial stage. [ABSTRACT FROM AUTHOR]

Can the extended mind explain the intentional behavior? Cleland argues that the extended mind theory forces us to give up our causal sovereignty when it comes to our actions, and therefore renders us not agentially responsible for them. If the extended mind theory is metaphysically incompatible with this very idea, the theory includes a deep inconsistency. The main reason for this is that the explanation on behavior by extended mind would not conform to Davidson's argument of "motivation-causality". However, Davidson's argument has its own drawbacks. It does not explain how meaning flows into behavior. A better approach is to reinterpret "the agential control" with the top-down causality. [ABSTRACT FROM AUTHOR]

Abstract This paper studies traveling waves of the (3+1)-dimensional Jimbo-Miwa equation comprehensively and systematically. By transforming its traveling wave system into a dynamical system in R 3 , we apply the bifurcation method of dynamical system to investigate its phase space geometry in detail and obtain the parameter bifurcation sets in which various types of bounded and unbounded traveling waves are identified and simulated. Furthermore, by calculating the complicated elliptic integrals, without any loss, we give exact expressions of all traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the bounded and unbounded ones. [ABSTRACT FROM AUTHOR]

Electrosurgery uses electric current to heat, coagulate and ligate tissue. The current flow induces a voltage due to the bio-impedance of the tissue. The flow of the current should be controlled precisely to avoid tissue damage by overheating. The control requires the proper mathematical formulation of the current and voltage relationship. This mathematical description can be explained as a dynamical system. It is composed of linear time invariant (LTI) system and/or the static nonlinearity. The in-depth understanding of the system behaviour requires parameter estimation of the LTI block and the nonlinearity. It is often done stepwise by identifying the best linear approximation (BLA) to fit the whole combination of LTI block and nonlinearity. In this paper, we study the potential discrimination of a block-oriented model between femoral, mesentery, renal and tendon tissue. The estimated system fits up to 99.84% accurately with the measured signal after optimization for the electrosurgery data of Covidien Inc. The parameters exhibit that a weak nonlinearity exists in the measurement data. Finally, the fractional order LTI systems are explored to cope with the diffusion due to the generated heat. • Mathematical formulation of the current-voltage relationship of bipolar electrosurgery • Differentiation among different types of tissue through the best linear approximation • Parametric study as the W-H system fits up to 99.84% on real-life electrosurgery data • Fractional-order LTI system is explored to cope with diffusion due to generated heat [ABSTRACT FROM AUTHOR]

A risk assessment for disasters is usually composed of hazard, vulnerability and exposure variables, which are hardly studied and modeled simultaneously. In volcanology, it remains ambitious to anticipate risk trajectories of pre- and post-eruption regimes. The interdependencies and feedback loops of the system's components, between geological, ecological, social and economic ones, give rise to trade-offs and synergies that should be disentangled for supporting decision-makers and helping local communities to face the risks. We developed here an innovative discrete-event and possibilistic model based on a dynamical network representation to assess volcanological multi-risk and long term post-eruption impacts of such a multifactorial system. We illustrated our method with the region around Mount Meru (Northern Tanzania), a strato-volcano with various eruption styles, located in a growing economic and touristic region (>1 M.inh.). We used qualitative and rule-based Petri nets, largely unused in environmental sciences, for an integrated assessment of the overall system dynamics and associated risks. As a central result, we showed that the region could recover from a blast eruption, irrespective of the timescale. Our study highlights the fact that agriculture and pastoralism remain key activities to favour the recovery of this region. Yet, as soon as subsidies from governmental and non-governmental organizations are lacking, the modeled region remains isolated from national and international activities and shifts to rural dynamics. Our case study can equip environmental risk assessment with innovative models, new dynamical indices (e.g. desirable and non-desirable trajectories), and rigorous reasoning for an ultimate integrated management of social-ecological systems at stake. • We integrated geological, ecological and socio-economic components/processes. • We developed innovative discrete-event and qualitative models. • We modeled exhaustive pre- and post-eruption trajectories of such systems. • This is a first application to multi-risk assessment in geology and environment. • Modeled systems confirmed the importance of rural activities for resilience. [ABSTRACT FROM AUTHOR]

This article is devoted to the mathematical modeling of vibration resistance of non-rigid shaft linear turning. The relevance of the study is based on the occurrence of vibration in machining non-rigid shafts, which are so intense that they force to significantly reduce the cutting mode, and to resort to multi-pass processing; they lead to premature cutting tool wear and, as a consequence, reduce the productivity of the part machining on metal-cutting machine-tools. In this regard, the purpose of this article is the establishment of appropriate mathematical models which describe the vibrations of the machine-tool elastic system under the influence of dynamic cutting forces generated during machining. The article presents methods of constructing a mathematical model closed to the process of non-free machine-tool dynamic system cutting at turning non-rigid shafts. The model takes different ways of mounting the workpiece on the machine-tool into account including the use of the damper. The basic theoretical principles to build a generalized mathematical model closed to the process on non-free machine-tool dynamic system cutting are substantiated herein. The regions of stability border for different types of technological equipment are revealed by the mathematical model developed. These mathematical models give an opportunity to reflect the complex processes that occur in a closed lathe dynamic system objectively to a greater degree. The article may be useful for engineers, scientists and students of engineering courses. [ABSTRACT FROM AUTHOR]

The main aim of this study was to introduce logical entropy on dynamical systems that their state spaces were sequential effect algebra. In this regard, logical partition was defined on sequential effect algebra and then based on logical partition concept, logical entropy on partitions, conditional logical entropy, and logical entropy on dynamical systems were introduced and their features were analyzed. In addition, it was proved that this entropy is an invariant object under isomorphism relation. [ABSTRACT FROM AUTHOR]

Building of adequate dynamical models of microblogging social networks is a topical task that is of interest from both theoretical and practical aspects. Experimental and theoretical results of studies related to choice of the adequate model are presented. The choice was made between two models: a nonlinear dynamical system and a nonlinear random dynamical system. By results of the fractal analysis of observable network time series and defining their probability density function it was established that the nonlinear random dynamical system was more adequate than the nonlinear dynamical system. The character of the observable time series was also explored. The possibility that microblogging social networks can be analyzed by means of Tsallis entropy and self-organized criticality is examined. [ABSTRACT FROM AUTHOR]

Mass balance of a glacier is an accepted measure of how much mass a glacier gains or loses. In theory, it is typically computed by integral functional and empirically, it is approximated by arithmetic mean. However, the variability of such an approach was not studied satisfactory yet. In this paper we provide a dynamical system of mass balance measurements under the constrains of 2nd order model with exponentially decreasing covariance. We also provide locations of optimal measurements, so called designs. We study Ornstein–Uhlenbeck (OU) processes and sheets with linear drifts and introduce K optimal designs in the correlated processes setup. We provide a thorough comparison of equidistant, Latin Hypercube Samples (LHS), and factorial designs for D- and K-optimality as well as the variance. We show differences between these criteria and discuss the role of equidistant designs for the correlated process. In particular, applications to estimation of mass balance of Olivares Alfa and Beta glaciers in Chile is investigated showing that simple application of full raster design and kriging based on inter- and extrapolation of points can lead to increased variance. We also show how the removal of certain measurement points may increase the quality of the melting assessment while decreasing costs. Blow-ups of solutions of dynamical systems underline the empirically observed fact that in a homogenous glaciers around 11 well-positioned stakes suffices for mass balance measurement. [ABSTRACT FROM AUTHOR]

The basic equations governing both physical and biological systems are non-linear. Therefore, it is not generally possible to obtain solutions of these systems analytically to decipher the observed complex dynamics. To understand the dynamics of a non-linear system, we use various numerical methods using computer. In this work, we use (a) power spectrum, (b) Poincar' esurface of section, (c) correlation dimension, (d) spectral and sample entropy method to understand the complex dynamics observed in simple non-linear systems, for example logistic map, Duffing oscillator, Lorenz system, Hindmarsh-Rose model in neuro-bioscience. We also describe methods to obtain visibility graph from a time series of a dynamical system and further use them to provide a network frame work for any dynamical system. [ABSTRACT FROM AUTHOR]

The long term outcome of Coronary Artery Bypass Graft (CABG) surgery remains unsatisfactory to this day. Despite years of improvements in surgical techniques and therapies administered, re-occlusion of the graft is experienced in 10-12% of the cases within just few months (Motwani JC, 1998). We suggest that an efficient post-surgical therapy might be found at the genetic level. Accordingly, we propose a multiscale model that is able to replicate the healing of the graft and detail the level of impact of targeted clusters of genes on the graft’s healing. A key feature of our integrated model is its capability of linking the genetic, cellular and tissue levels with feedback bridges in such a way that every single variation from an equilibrium point is reflected on all the other elements, creating a highly organized loop. Once validated on experimental data, our model offers the possibility to test several gene therapies that aim to improve the patency of the graft lumen in advance. Being able to anticipate the outcome will speed up the development of an efficient therapy and may lead to prolonged life expectancy of the graft. [ABSTRACT FROM AUTHOR]

This study is used to investigate the exact explicit solutions and dynamical behaviors of the (1+1)-dimensional integrable system of Drinfel'd–Sokolov–Wilson equations in dispersive media. Firstly, the unified method is implemented to find explicit solutions in polynomial and rational forms. These solutions include rational, dark and bright soliton structures. After that, the planar dynamical system of the considered model is obtained using the Galilean transformation. The phase portraits of the bifurcations are drawn from the planar dynamical system for different physical parametric values using the fourth-order Runge–Kutta method. Further, an external force is imposed on the dynamical system to observe the phase portraits of chaotic trajectories. These tracks are outlined for different values of the strength and frequency of the external force acting on the dynamical system. The outcomes show that a given model has chaotic behvior as its solution becomes disordered by taking small variation in the strength and frequency of the external force. The results are new and can be helpful in investigating the dynamical behaviors of the other nonlinear physical models arising in optics, bio-mathematics and so many other fields of science. • Soliton structures and dynamical behavior. • Drinfel'd–Sokolov–Wilson equations in dispersive media. • Fourth-order Runge–Kutta method. [ABSTRACT FROM AUTHOR]

We investigate the flat-FRW model in the dynamical Chern–Simons gravity with interacting dark energy. We use dynamical system analysis to illustrate the outcomes of the model. The model yields late-time accelerating universe with decelerating past having matter, radiation and stiff matter dominated phases. The modification term of the Chern–Simons gravity gives a nontrivial impact on the cosmological evolution of universe in the model. We recast the cosmological equations into the autonomous system and investigate the fixed points, eigenvalues and stability of the model. The model possess an attractor corresponding to the accelerated expansion at late-times, compatible with the observations. The evolution of cosmological parameters like deceleration parameter, effective equation of state parameter, state-finder diagnostic analysis and classical stability of the model have been discussed in detail. We show that the model possess decelerating past originating with stiff-matter like evolution, further evolving into radiation and/or matter dominated phases with late-time accelerating universe evolution as ultimate fate, on the basis of model parameter values. The model is classically stable in nature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the isomorphisms of the category of all subgroupoids of trivial groupoids on various sets X with group ℤ. We also provide Maple procedures for obtain simplified models of a discrete dynamical system seen as a subgroupoid a trivial groupoid with group ℤ. [ABSTRACT FROM AUTHOR]

The purpose of this short note is to prove that if the category of all subgroupoids of trivial groupoids with group Z is seen as a model category M in the sense [M. Nielsen A. Joyal and G. Winskel, 1996] and [E. Haghverdi, P. Tabuada, G.J. Pappas, 2002], then we can highlight a path category P (a subcategory of M serving as an abstract notion of time) such that the P-open morphisms are exactly the groupoid homomorphisms. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the isomorphisms of the category of all subgroupoids of trivial groupoids on various sets X with group Z. We also provide Maple procedures for obtain simplified models of a discrete dynamical system seen as a subgroupoid a trivial groupoid with group Z. [ABSTRACT FROM AUTHOR]

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The article deals with set-valued estimation of dynamical system state when there is no statistical information about the initial state, disturbances and noises but the sets of their possible values are available. In some cases we can have additional information about disturbance dynamics that can improve the accuracy of the estimates. The article describes set-valued estimation algorithm when disturbance is decomposed as a system of functions with unknown coefficients. The comparison of estimates for the case when the kind of decomposition is known and the case when only a set of possible values is available is performed. [ABSTRACT FROM AUTHOR]

This work aims to demonstrate a rather specific "iterative nature" existing in a class of regular economic dynamics by revisiting two typical economic concepts as informative examples, viz., random utility and stochastic growth. We begin with a formal treatment of discrete dynamical system and its popular derivation, iterated function system, so that a solid foundation could be laid for our analysis of economic dynamics. Two economic systems afterwards are constructed to show how random utility function and stochastic growth in a classical economy could be essentially driven by some iterative elements. Besides, our analyses also implicitly show that a quite complex economic dynamics carrying substantial randomness could basically originate in some fairly simple dynamic principles. [ABSTRACT FROM AUTHOR]

In this article, we investigate the bifurcation and chaos in a simplest fractional-order memristor-based electrical circuit composed of only three circuit elements: a linear passive capacitor, a linear passive inductor and a non-linear active memristor with two-degree polynomial memristance and a second-order exponent internal state. It is shown that this fractional circuit can exhibit a drastically rich non-linear dynamics such as a Hopf bifurcation, coexistence of two, three and four limit cycles, double-scroll chaotic attractor, four-scroll chaotic attractor, coexistence of one (or two) chaotic attractor with one limit cycle and new chaotic attractor which is not observed in the integer case. Finally, the presence of chaos is confirmed by the application of the recently introduced 0-1 test. [ABSTRACT FROM AUTHOR]

Abstract: Within cognitive, affective and social neuroscience more and more mechanisms are found that suggest how emotions relate in a bidirectional manner to many other mental processes and behaviour. Based on this, in this paper a neurologically inspired dynamical systems approach on the dynamics and interaction of emotions is discussed. Thus an integrative perspective is obtained that can be used to describe, for example, how emotions relate to feelings, beliefs, desires, experiences, decision making, and to emotions of others. It is pointed out how this perspective can be used to obtain integrated computational models of such mental processes incorporating emotions. [Copyright &y& Elsevier]

Abstract: Clinical analysis of the electromyogram is a powerful tool for diagnosis of neuromuscular diseases. Therefore, the classification of electromyogram signals has attracted much attention over the years. Several classification methods based on techniques such as neuro-fuzzy systems, wavelet coefficients, and artificial neural networks have been investigated for electromyogram signal classification. However, many of these time series analysis methods are not highly successful in classification of electromyography signals due to their complexity and non-stationarity. In this paper, we introduce a novel approach for the diagnosis of neuromuscular disorders using recurrence quantification analysis and support vector machines. Electromyogram signals are transformed into recurrence plots and a set of statistical features are extracted using recurrence quantification analysis. Support vector machine employing radial basis functions is used for classifying the normal and abnormal of neuromuscular disorders. Examining the acoustic patterns in electromyogram, we classify the signals into one of the three categories: healthy, neuropathy, and myopathy. The results show that the proposed method classifies these signals with 98.28% accuracy; it is a significantly better accuracy than what has been reported in the literature thus far. The accurate results indicate that proposed diagnosis method of neuromuscular disorders is very effective. [Copyright &y& Elsevier]

A dynamical system concerning intracellular substances and transport patterns was proposed to describe glycerol bioconversion to 1, 3-propanediol in continuous fermentation process. Some properties of the system were subsequently discussed. Taking the error between the computational values and experimental data as the cost function, a parameter identification model to identify the intracellular kinetic parameters was established. The existence of the optimal parameters in the parameter identification model was also proved. Finally, an improved particle swarm optimization was constructed to solve the above parameter identification model. Numerical results show that the mean relative error is cut down by 20. 635 %, and the proposed algorithm has higher global convergence compared with other optimization algorithms. [ABSTRACT FROM AUTHOR]

Abstract: Modeling and simulation of nonlinear systems under chaotic behavior is presented. Nonlinear systems and their relation to chaos as a result of nonlinear interaction of different elements in the system are presented. Application of chaotic theory for power systems is discussed through simulation results. Simulation of some mathematical equations, e.g. Vander Pol''s equation, Lorenz''s equation, Duffing''s equation and double scroll equations are presented. Theoretical aspects of dynamical systems, the existence of chaos in power system and their dependency on system parameters and initial conditions using computer simulations are discussed. From the results one can easily understand the strange attractor and transient stages to voltage collapse, angle instability or voltage collapse and angle divergence simultaneously. Important simulation results of chaos for a model three bus system are presented and discussed. [Copyright &y& Elsevier]

Prediction of trends for time series is investigated by the dynamical systems methods. Several methods of extracting the trends of time series are compared by the aid of the error measurement model derived from Copula functions. The constructing method of the comparison criterion is innovated. Using the trends of time series data,the prediction of the stock market index through the dynamical system demonstrates the validity of this method. [ABSTRACT FROM AUTHOR]

In this paper we deal with the product of two dynamical systems. We give some results related to properties of a point in the product dynamical system and show wheather these properties also hold in the factor dynamical systems. We investigate the relationship between a point. (p0,q0) in the product system and corresponding points p0,q0 in the factor system, first when the phase space is metric and then when the phase space is a topological space. [ABSTRACT FROM AUTHOR]

This work deals with modeling and fault detection and identification for robot manipulator. We have used for a dynamical system a hybrid approach. The model is decomposed into two parts: first, a certain part modeled using classical analytical theory and it is preferable to be linear. Second, an uncertain part representing the nonlinearities neglected in the first part, which is modeled using neuro-fuzzy modeling. Both analytical redundancy and neuro-fuzzy modeling are used to improve robustness. The analytical redundancy is used to generate residuals for the fault detection and location procedure. The neuro-fuzzy modeling is used to model modeling errors and faults, which allows performing the robustness and the sensitivity. Thanks to neurofuzzy modeling the errors of modeling are compensated and the faults are well identified as it is shown through the results of simulation. [ABSTRACT FROM AUTHOR]

The robustness and the fragility of a second-order SODE is studied by means of the five KCC invariants, which provide information on the Jacobi stability ([1, 8, 53, 14]). The paper presents a brief overview on Finslerian m-root metrics, in particular, of Berwald-Moor type, and applies the developed theory to a Berwald-Moor type conformally deformed relativistic model, where the five KCC invariants of the Finslerian framework are computed by means of the MAPLE 12 symbolic software. [ABSTRACT FROM AUTHOR]

Abstract: Natural ventilation systems may have multiple steady states in the combined buoyancy and wind driven mode in a single space. In this paper, dynamical system analysis is applied both graphically and quantitatively to investigate the multiple steady state behavior of such a natural ventilation system. The necessary conditions for the system to have multiple steady states are derived for a single space combined wind and buoyancy driven natural ventilation system. Distinct from previous studies, the derivation comes from the transient dynamical system behaviors of the system rather than from the steady state equations, and it can be applied to more general cases. Based on the dynamical system analysis, the quantitative relation between the initial temperature and the final steady state is investigated for the single space case. The unstable steady state, which cannot physically exist in reality, is the critical point of the initial value in determining the final (steady) state of the system. [Copyright &y& Elsevier]

Abstract: Natural ventilation systems may have multiple steady states in the combined buoyancy and wind driven mode due to the nonlinearity of the systems. Previous studies have shown that some of the steady states are locally stable for small disturbances. However, the system can flip over from one stable steady state to another under sufficiently strong perturbations. In this paper, the mechanism of such state transitions is quantitatively investigated by a dynamical system approach. The transition dynamics between the stable steady states is examined by the system''s responses to two types of perturbations—heat source fluctuations and wind variations. Two important parameters—the minimum perturbation magnitude and the minimum perturbation time to switch from one stable steady state to another—are defined to describe the transition requirements. The result from a previous experimental study was discussed and explained by these state transition behaviors. The transition dynamics between two stable steady states under perturbations are found important to the robustness of the stable steady states, which can be quantitatively described by the minimum perturbation time and the minimum perturbation magnitude. The experimental and numerical simulation results from another existing study are successfully explained by these two parameters. The applications of the developed perturbation method are further discussed. [Copyright &y& Elsevier]

Abstract: Consider an asymptotically stable linear semigroup of class , acting on a Banach space . By shifting the action of we obtain an affine semigroup with an arbitrary point as a sink. Selecting a specific set of sinks and combining the action of the corresponding semigroups gives rise to a multimodal control system which, after constraining the action of each mode, becomes a hybrid system with switching. We prove the existence of a globally attracting compact set and describe its structure. In the case of the constrained system we use this structure to prove the convergence of ergodic averages–such as the average time between switches–for a certain generic set of solutions. Next we turn to the bimodal case, typical of thermostatic control. We review a series of results where the existence of a periodic solution (with two periodic switches) has been shown. On the other hand, we announce a finite-dimensional example where no such solution exists. [Copyright &y& Elsevier]

A numerical gradient algorithm was proposed to solve a constrained optimization problem arising from a nearestness problem in SO(n), which can be viewed as a discrete dynamical system algorithm. The main advantage of the method is that the iterative sequence always satisfies the constrained condition. The convergence analysis and asymptotical stability analysis were established, and the numerical experiments show the effectiveness and reliability of the algorithm. [ABSTRACT FROM AUTHOR]

Many problems in computational biology consist in the time-dependent observation of gene expression data. Here, the application of modern methods from dynamical systems, optimization theory, numerical algorithms and the utilization of implicit discrete information lead to a deeper understanding. In [5], we began our research by representing the behavior of gene expression pattern by a system of ordinary differential equations, which we analytically and algorithmically investigated under the parametrical aspect of stability or instability. Our algorithm strongly exploited combinatorial information.We present a discrete approximation problem and a solution for the mixed integer problem which occur when we restrict the solution space. [Copyright &y& Elsevier]

In this paper, we study the late time cosmology of a non-canonical scalar field (k -essence) coupled to a vector field in a Bianchi-I background. Specifically, we study three cases: canonical scalar field (quintessence) with exponential potential as a warm up, the dilatonic ghost condensate, and the Dirac Born Infeld field with exponentials throat and potential. By using a dynamical system approach, we show that anisotropic dark energy fixed points can be attractors for a suitable set of parameters of each model. We also numerically integrate the associated autonomous systems for particular initial conditions chosen in the deep radiation epoch. We find that the three models can give an account of an equation of state of dark energy close to − 1 nowadays. However, a non-negligible spatial shear within the current observational bounds is possible only for the quintessence and the Dirac Born Infeld field. We also find that the equation of state of dark energy and the shear oscillate at late times, whenever the coupling of the k -essence field to the vector field is strong enough. The reason of these oscillations is explained in the appendix. [ABSTRACT FROM AUTHOR]

• A data-driven approach based on the Koopman theory is developed. • The dynamics of complex dynamical system can be discovered and visualized in an intrinsic space. • The proposed method is successfully applied to the anomaly detection problem of epileptic seizure onsets using multi-variate EEG signals. For most real-life dynamical systems, it is difficult to explicitly identify evolution rules or functions that describe the complex, non-linear, and non-stationary patterns of dynamical systems. Alternatively, it is common to describe and analyze the system dynamics through observations, e.g., electroencephalography (EEG) signals are observed and used for representing the brain system. Even though, the underlying dynamics of the system is still not easily uncovered and displayed as a whole. In this study, we propose a data-driven approach based on the Koopman operator to reconstruct and analyze the underlying dynamics of dynamical systems by representing them in a linear intrinsic space. To demonstrate the applicability, we apply the proposed method to dynamical pattern recognition problems, and validate it with a simulation study of the Lorenz system and a brain disorder of epileptic seizure using multi-variate EEG signals. Furthermore, we introduce a new measurement that is derived from the reconstructed dynamics associated with the attractor of the system in the Koopman intrinsic space. The experimental results conclude the effectiveness of the proposed method for anomaly detection using the reconstructed dynamical information. [ABSTRACT FROM AUTHOR]