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The dynamics of the tubular chemical reactor with mass recycle was examined. In such a system, temperature and concentrations may oscillate chaotically. This means that state variable values are then unpredictable. In this paper, it has been shown that despite the chaos, the behavior of such a reactor can be predictable. It has been shown that this phenomenon can occur in two cases. The first case concerns intermittent chaos. It has been shown that intermittent outbursts can occur at regular intervals. The second case concerns transient chaos, i.e. a situation when chaos occurs only for a certain period of time, e.g. only during start-up. This phenomenon makes it impossible to predict what will occur in the reactor in the nearest time, but, makes it possible to precisely determine the values of the variables even in the distant future. Both of these phenomena were tested by numerical simulation of the mathematical model of the reactor. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new four-dimensional hyperchaotic system derived from the chaotic maps of Peter de Jong's simple attractor and the discrete iterative function. In this work, our main motivation is to explore a link that can be developed to generate hyperchaos from 2D chaotic system. An association between 2D system and a higher order one was not studied in the previous literature. In fact, in the literature, there is no two-dimensional systems from which we are able to associate a four-dimensional one. In this context, a special interest is reserved to Peter de Jong system due to its exceptional advantages such as hypersensitivity and velocity. The challenge in this paper is the development of a four-dimensional hyperchaotic system associated to the Peter de Jong one while conserving its important characteristics such as hypersensitivity, velocity and the lack of equilibrium. The system structure that we will detail is different from other hyperchaotic systems widely suggested in the literature. In fact, the proposed attractor does not display any equilibrium point. A mathematical study is carried out in order to obtain time plots, Lyapunov exponents spectrum and bifurcation diagram. Finally, we will prove the high sensitivity of this system relative to its initial condition by simulations and experimental observations. [ABSTRACT FROM AUTHOR]

A wide variety of spatio-temporal models are available in literature which are unable to generate stationary patterns through Turing bifurcation. Introduction of nonlocal terms to the same model can produce Turing patterns and this is true even for a single species population model. In this paper, we consider a prey–predator model of Holling–Tanner type with a generalist predator and a nonlocal interaction in the intra-specific competition term of the prey population. Nonmonotonic functional response is assumed to describe consumption rate of the prey by the predator. The Turing instability condition has been studied for the model without the nonlocal term around coexisting steady states. We also determine the Turing domain in the presence of nonlocal interaction term. The spatial-Hopf bifurcation has been studied and it plays an important role to find the pure Turing domain for the nonlocal model. Furthermore, in the presence of nonlocal interaction, the nonlocal model produces traveling wave solution. Using linear stability analysis, we have obtained the wave speed for the traveling wave front analytically. With the help of numerical simulation, we have verified that the speed of the traveling wave front for the complete nonlinear nonlocal model matches with the analytical approximation. The emergence of wave trains has also been established for higher range of nonlocal interaction. [ABSTRACT FROM AUTHOR]

The broadcast of awareness programs through TV and radio advertisements (ads) makes people aware and brings behavioral changes among the individuals regarding the risk of infection and its control mechanisms. In this paper, we propose and analyze a nonlinear mathematical model for the control of infectious diseases due to impact of TV and radio advertisements. It is assumed that susceptible individuals are vulnerable to infection as well as information through TV and radio ads and they contract infection via direct contact with infected individuals. In the model formulation, it is also assumed that the growth rates in cumulative number of TV and radio ads are proportional to the number of infected individuals with decreasing function of aware individuals. Further, it is assumed that awareness among susceptible individuals induces behavioral changes and they form separate aware classes, which are fully protected from infection as they use precautionary measures for their protection during the infection period. The feasibility of equilibria and their stability properties are discussed. It is shown that the augmentation in dissemination rate of awareness among susceptible individuals due to TV and radio ads may cause stability switches through Hopf-bifurcation. The analytical findings are supported through numerical simulations. [ABSTRACT FROM AUTHOR]

The analysis of delay dynamics (DD) is the basic big picture in networked control systems (NCS) research since the knowledge of its behavior may improve the design of more robust controllers, and consequently, the system performance. However, the extreme complexity of modern communications and networks, coupled with their traffic characteristics, makes the characterization of their performance through analytical models a difficult task. Relying on fractional calculus (FC), this paper studies the dynamics of IP delays and attempts to clarify the most important features of network traffic, providing the reader some connections between traffic in communication networks and FC. Likewise, a fractional order model of DD is presented based on a survey of current network traffic models. Some simulations are given to validate the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamical behavior of a prey-dependent digestive model with a state-dependent impulsive effect. Using the Poincaré map and the Lambert W-function, we find the analytical expression of discrete mapping. Sufficient conditions are established for transcritical bifurcation and period-doubling bifurcation through an analytical method. Exact locations of these bifurcations are explored. Numerical simulations of an example are illustrated which agree well with our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the nonlinear dynamic behavior of an electro-mechanical vibration absorber (NEVA), taking into account a modified (MR) Damper (MRD), in its mathematical model, which was excited by a nonideal motor (NIS), by using perturbation analysis and numerical simulations. [ABSTRACT FROM AUTHOR]

Computer simulation of mathematical models of mammalian ventricular myocytes has become a very promising tool for understanding the underlying mechanisms of cardiac arrhythmias and may provide useful predictions of treatment in order to prevent fatal arrhythmias. In this paper, we employ the Luo-Rudy (LR) model of membrane action potential of the mammalian ventricular cell. Simulation is performed with the aid of a direct method for locating the equilibria and by an adaptive grid method for constructing bifurcation diagrams. Two-parameter bifurcation diagrams are constructed to show the parameter sets in which (a) spontaneous oscillations exist, (b) the equilibrium corresponding to the resting potential is stable, or (c) the equilibrium with the most depolarized potential is stable. Multiple attractors are detected near the boundary of these parameter sets. The generation of normal and abnormal pacemaking activities is elucidated via bifurcation analysis. Spontaneous oscillations appear and disappear via saddle-node homoclinic bifurcations, Hopf bifurcations, homoclinic bifurcations, or fold bifurcations of limit cycles. Limit cycles may become chaotic via period-adding cascades as the extracellular potassium concentration [K]o decreases. Pacemaking activities may also be generated when the time-independent potassium current is blocked. [ABSTRACT FROM AUTHOR]

In this paper the global patterns that result from local interactions between players on a two-dimensional lattice are studied. The assumptions on interaction between players are based on the Prisoner's Dilemma game that has been used extensively in game theory and in the study of biological systems. Each player is located on a square lattice, and is assumed to cooperate or defect, based on mimicking the neighbor with the highest cumulative score from the preceding round of play. The edges of the lattice are glued to form a torus. Computer simulations are conducted for different sized lattices, different payoff values, and different initial conditions. Though the paper is primarily concerned with player behavior without self-interaction, some results with self-interaction are also included. The influence of "ideal" cooperators on the evolution of the system dynamics is also studied. Three generic regimes of behavior are identified. Complex global patterns with complicated dynamics and sometimes unpredictable results occur. Steady-state solutions, simple and complex periodic solutions, and traveling waves are observed depending on the initial conditions and the payoff values. [ABSTRACT FROM AUTHOR]

The pre-Bötzinger complex of the mammalian brain stem plays a crucial role in the respiratory rhythms generation. Neurons within the pre-Bötzinger complex have been found experimentally to yield different firing activities. In this paper, we study the spiking and bursting activities related to the respiratory rhythms in the pre-Bötzinger complex based on a mathematical model proposed by Butera. Using the one-dimensional first recurrence map induced by dynamics, we investigate the different bursting patterns and their transition of the pre-Bötzinger complex neurons based on the Butera model, after we derived a one-dimensional map from the dynamical characters of the differential equations, and we obtained conditions for the transition of different bursting patterns. These analytical results were verified through numerical simulations. We conclude that the one-dimensional map contains similar rhythmic patterns as the Butera model and can be used as a simpler modeling tool to study fast-slow models like pre-Bötzinger complex neural circuit. [ABSTRACT FROM AUTHOR]

A three-dimensional discrete-time Hindmarsh-Rose model obtained by the forward Euler scheme is investigated in this paper. When the integral step size is chosen as a bifurcation parameter, conditions of existence for the fold bifurcation, the flip bifurcation, and the Hopf bifurcation are derived by using the center manifold theorem, bifurcation theory and a criterion of Hopf bifurcation. Numerical simulations including time series, bifurcation diagrams, Lyapunov exponents, phase portraits show the consistence with the analytical analysis. Our research results demonstrate that the integral step size makes a difference corresponding to local and global bifurcations of the three-dimensional discrete-time Hindmarsh-Rose model. These results can supply a solid analytical basis to the study of Hindmarsh-Rose model, and it is necessary to illustrate how much the integral step size is adopted in advance when numerical solutions or approximate solutions of the original continuous-time model is concerned. [ABSTRACT FROM AUTHOR]

The noise induced stochastic behaviors, in terms of stochastic resonance (SR) and coherence resonance (CR), have been widely reported in many nonlinear systems in different disciplines. In particular, in neuroscience, both the phenomena of SR and CR have been discovered. However, the traditional studies only focus on the dynamical behaviors of the neurons without considering the effects of other biological cells. It is known that neurons are surrounded by a number of glial cells. Being a subgroup of glial cells, astrocytes have been argued to take part in neuronal signal processing. Therefore, it is more reasonable to study the dynamics of a neuron by incorporating the effect of astrocyte, which is termed as dressed neuron. In this paper, the stochastic behaviors of a dressed Hodgkin-Huxley neuron with mutual neuron-astrocyte interaction are studied, and the effects of astrocyte on different resonance mechanisms are analyzed. Simulation results show that the astrocyte plays a similar role as noise in the stochastic behaviors of a neuron, which enhances the performance of a neuron in signal transduction via resonance mechanisms. [ABSTRACT FROM AUTHOR]

The bifurcation analysis of a predator-prey system of Holling and Leslie type with constant-yield prey harvesting is carried out in this paper. It is shown that the model has a Bogdanov-Takens singularity (cusp case) of codimension at least 4 for some parameter values. Various kinds of bifurcations, such as saddle-node bifurcation, Hopf bifurcation, repelling and attracting Bogdanov-Takens bifurcations of codimensions 2 and 3, are also shown in the model as parameters vary. Hence, there are different parameter values for which the model has a limit cycle, a homoclinic loop, two limit cycles, or a limit cycle coexisting with a homoclinic loop. These results present far richer dynamics compared to the model with no harvesting. Numerical simulations, including the repelling and attracting Bogdanov-Takens bifurcation diagrams and corresponding phase portraits, and the existence of two limit cycles or an unstable limit cycle enclosing a stable multiple focus with multiplicity one, are also given to support the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper proposes to use a state feedback method to control the Hopf bifurcation for a novel congestion control model, i.e. the exponential random early detection (RED) algorithm with a single link and a single source. The gain parameter of the congestion control model is chosen as the bifurcation parameter. The analysis shows that in the absence of the state feedback controller, the model loses stability via the Hopf bifurcation early, and can maintain a stationary sending rate only in a certain domain of the gain parameter. When applying the state feedback controller to the model, the onset of the undesirable Hopf bifurcation is postponed. Thus, the stability domain is extended, and the model possesses a stable sending rate in a larger parameter range. Furthermore, explicit formulae to determine the properties of the Hopf bifurcation are obtained. Numerical simulations are given to justify the validity of the state feedback controller in bifurcation control. [ABSTRACT FROM AUTHOR]

In this paper, we study HIV mathematical models with treatments. Two models with RT inhibitor and HIV protease inhibitor are studied. Local and global analysis is carried out. By identifying a critical number for both treatments, we show that if the treatment is at least effective, then the uninfected steady state P0 is the only equilibrium in the feasible region, and P0 is globally asymptotically stable. Therefore, no HIV infection persists and infected T cells and HIV virus are cleared over time. However, if the treatment is not effective enough, i.e. less than , then a unique infected steady state P* emerges in the interior of the feasible region. P0 becomes unstable and the system is uniformly persistent. Therefore, HIV infection persists. In this case, the unique infected steady state can be either stable or unstable. We show that it is locally stable only for r (the proliferation rate of T cells) small or large and unstable for some intermediate values. Global stability result is established for small values of r. Numerical simulation shows that once P* becomes unstable, periodic solution appears. [ABSTRACT FROM AUTHOR]

Variable-order fractional diffusion equation model is a recently developed and promising approach to characterize time-dependent or concentration-dependent anomalous diffusion, or diffusion process in inhomogeneous porous media. To further study the properties of variable-order time fractional subdiffusion equation models, the efficient numerical schemes are urgently needed. This paper investigates numerical schemes for variable-order time fractional diffusion equations in a finite domain. Three finite difference schemes including the explicit scheme, the implicit scheme and the Crank-Nicholson scheme are studied. Stability conditions for these three schemes are provided and proved via the Fourier method, rigorous convergence analysis is also performed. Two numerical examples are offered to verify the theoretical analysis of the above three schemes and illustrate the effectiveness of suggested schemes. The numerical results illustrate that, the implicit scheme and the Crank-Nicholson scheme can achieve high accuracy compared with the explicit scheme, and the Crank-Nicholson scheme claims highest accuracy in most situations. Moreover, some properties of variable-order time fractional diffusion equation model are also shown by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonlinear response of the nonlinear mass-spring model with nonsmooth stiffness. For this purpose, we take as prototype model, a system that consists of the double-well smooth potential with an additional spring component acting on the system only for large enough displacement. We focus our study on the analysis of the homoclinic orbits for such nonlinear potential for which we observe the appearance of chaotic motion in the presence of damping effects and an external harmonic force, analyzing the crucial role of the linear spring in the dynamics of our system. The results are shown by using both the Melnikov analysis and numerical simulations. We expect our work to have implications on problems concerning the suspension of vehicles, among others. [ABSTRACT FROM AUTHOR]

The study of chemical reactions with oscillating kinetics has drawn increasing interest over the last few decades because it also contributes towards a deeper understanding of the complex phenomena of temporal and spatial organizations in biological systems. The Cellular Nonlinear Network (CNN) local activity principle introduced by Chua [1997, 2005] has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice formed by coupled cells. Recently, Yang and Epstein proposed a reaction–diffusion Oregonator model with five variables for mimicking the Belousov–Zhabotinskii reaction. The Yang–Epstein model can generate oscillatory Turing patterns, including the twinkling eye, localized spiral and concentric wave structures. In this paper, we first propose a modified Yang–Epstein's Oregonator model by introducing a controller, and then map the revised Oregonator reaction–diffusion system into a reaction–diffusion Oregonator CNN. The Oregonator CNN has two cell equilibrium points Q1 = (0, 0, 0, 0, 0) and Q2, representing the "original" equilibrium point and an additional equilibrium point, respectively. The bifurcation diagrams of the Oregonator CNN are calculated using the analytical criteria for local activity. The bifurcation diagrams of the Oregonator CNN at Q1 have only locally active and unstable regions; and the ones at Q2 have locally passive regions, locally active and unstable regions, and edge of chaos regions. The calculated results show that the parameter groups of the Oregonator CNN which generate complex patterns are located on the edge of chaos regions, or on locally active unstable regions near the edge of chaos boundary. Numerical simulations show also that the Oregonator CNNs can generate similar dynamics patterns if the parameter groups are selected the same as those of the Yang–Epstein model. In particular, the parameters of the Yang–Epstein model which exhibit twinkling-eye patterns, and pinwheel patterns are located on the edges of chaos regions near the boundaries of locally active unstable regions with respect to Q2. The parameters of the Yang–Epstein models which exhibit labyrinthine stripelike patterns are located on the locally active unstable regions near the boundaries of the edge of chaos regions with respect to Q2. However the parameter group of the Yang–Epstein model with isolated spiral patterns is in the locally passive region near the boundary with edge of chaos with respect to Q2, whose trajectories tend to the equilibrium point Q2. Choosing a kind of triggering initial conditions given in [Chua, 1997], and the parameters of the Oregonator equations with the twinkling-eye patterns, pinwheel patterns, labyrinthine stripelike patterns, and isolated spiral patterns, three kinds of new spiral waves generated by the Oregonator CNNs were observed by numerical simulations. They seem to be essentially different patterns to those generated by the Oregonator CNNs with initial conditions consisting of equilibrium points plus small random perturbations. Our results demonstrate once again Chua's assertion that a wide spectrum of complex behaviors may exist if the corresponding CNN cell parameters are chosen in or near the edge of chaos region. [ABSTRACT FROM AUTHOR]

This paper reveals the dynamics of a delayed neural network of four neurons, with a short-cut connection through a theoretical analysis and some case studies of both numerical simulations and experiments. It presents a detailed analysis of the stability and the stability switches of the network equilibrium, as well as the Hopf bifurcation and the bifurcating periodic responses on the basis of the normal form and the center manifold reduction. Afterwards, the study focuses on the validation of theoretical results through numerical simulations and circuit experiments. The numerical simulations and the circuit experiments not only show good agreement with theoretical results, but also show abundant effects of the short-cut connection on the network dynamics. [ABSTRACT FROM AUTHOR]

In a normal power system, many generators are operating in synchrony. That is, they all have the same speed or frequency, the system frequency. In case some accident occurs, a situation might arise in which one or more generators are running at a different speed, much faster than the system frequency. They are said to be running away or stepping out, or in a state of accelerated stepping out. We have been engaged in a series of studies of this situation, and have found global attractor-basin portraits. In the course of this program, we have observed the phenomenon of decelerated stepping out, in which one or more generators deviate from the system frequency toward lower speeds. These kinds of behavior cannot be explained with the well-known model involving one generator operating on to an infinite bus. Rather, we require a model in which robust subsystems — for example, generator/motor combination, which we call swing pairs — are connected by interconnecting transmission lines. In this more general context, the deviant behaviors we are considering may be regarded as forms of desynchronization of subsystems. We therefore begin this paper with the derivation of a new mathematical model, in which there is no infinite bus nor fixed system frequency. In the simple case of two subsystems (each a swing pair) weakly coupled by an interconnecting transmission line, we develop a system of seven differential equations which include the variation of frequency in a fundamental way. We then go on to study the behavior of this model, using our usual methods of computer simulation to draw the attractor-basin portraits. We have succeeded in finding both accelerated and decelerated stepping out in this new model. In addition, we discovered an unexpected subharmonic swinging of the whole system. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of obtaining stable and robust oscillations of underactuated mechanical systems. It is concerned with the Hopf bifurcation analysis of a Controlled Inertia Wheel Inverted Pendulum (C-IWIP). Firstly, the stabilization was achieved with a control law based on the Interconnection, Damping, Assignment Passive Based Control method (IDA-PBC). Interestingly, the considered closed-loop system exhibits both supercritical and subcritical Hopf bifurcation for certain gains of the control law. Secondly, we used the center manifold theorem and the normal form technique to study the stability and instability of limit cycles emerging from the Hopf bifurcation. Finally, numerical simulations were conducted to validate the analytical results in order to prove that with IDA-PBC we can control not only the unstable equilibrium but also some trajectories such as limit cycles. [ABSTRACT FROM AUTHOR]

A generic Turing type reaction-diffusion system derived from the Taylor expansion near a con-stant equilibrium is analyzed. The existence of Hopf bifurcations and steady state bifurcations is obtained. The bifurcation direction and the stability of the bifurcating periodic obits are calculated. Numerical simulations are included to show the rich spatiotemporal dynamics. [ABSTRACT FROM AUTHOR]

A nonlinear state feedback controller is proposed for the generation of chaos in third-order linear autonomous continuous time systems. With a simple feedback controller of the form g(x)=βx|x|, chaotic dynamics can be observed. Bifurcation analysis and the verification of the existence of chaos are given based on numerical continuation techniques and the Shil'nikov theorem. Both computer simulation and circuit implementation demonstrate the chaotification effect of this simple feedback controller. [ABSTRACT FROM AUTHOR]

Dynamic behavior of a discrete-time prey–predator system with Leslie type is analyzed. The discrete mathematical model was obtained by applying the forward Euler scheme to its continuous-time counterpart. First, the local stability conditions of equilibrium point of this system are determined. Then, the conditions of existence for flip bifurcation and Neimark–Sacker bifurcation arising from this positive equilibrium point are investigated. More specifically, by choosing integral step size as a bifurcation parameter, these bifurcations are driven via center manifold theorem and normal form theory. Finally, numerical simulations are performed to support and extend the theoretical results. Analytical results show that an integral step size has a significant role on the dynamics of a discrete system. Numerical simulations support that enlarging the integral step size causes chaotic behavior. [ABSTRACT FROM AUTHOR]

We consider population dynamics of agents who can both play the cooperative strategy and the competition strategy but ignore whether the game to come will be cooperative or noncooperative. For that purpose, we propose an evolutionary model, built upon replicator(–mutator) dynamics under strategic uncertainty, and study the impact of update decay. In replicator–mutator dynamics, we find that the strategy replication under certain mutation in an unstructured population is equivalent to a negative strategy replication in a structured population. Likewise, in replicator–mutator dynamics with decay, the strategy replication under certain mutation in a structured population is equivalent to a negative replication issued from an unstructured population. Our theoretical statements are supported by numerical simulations performed on bifurcation diagrams. [ABSTRACT FROM AUTHOR]

This study is devoted to the revelation of the dynamical mechanisms of cell growth in response to antibiotics. We establish a mathematical model of ordinary differential equations for an antibiotic-resistant growth system with one positive feedback loop. We perform a dynamical analysis of the behavior of this model system. We present adequate sets of conditions that can guarantee the existence and stability of biologically-reasonable steady states. Using bifurcation analysis and numerical simulation, we show that the relative growth rate, which is defined as the ratio of the cell growth rate to the basal cell growth rate in the absence of antibiotics, can exhibit bistable behavior in an extensive range of parameters that correspond to a growth state and a nongrowth state in biology. We discover that both antibiotic and antibiotic resistance genes can cooperatively enhance bistability, whereas the cooperative coefficient of feedback can contribute to the onset of bistability. These results would contribute to a better understanding of not only the evolution of antibiotics but also the emergence of drug resistance in other diseases. [ABSTRACT FROM AUTHOR]

Two different bifurcation scenarios of spontaneous neural firing patterns with decreasing extracellular calcium concentrations were observed in the biological experiment on identical pacemakers when potassium concentrations were fixed at two different levels. Six typical experimental scenarios manifesting dynamics closely matching those previously simulated using the Hindmarsh-Rose model and Chay model are provided as representative examples. Bifurcation scenarios from period-1 bursting to period-1 spiking via a complex process and via a simple process, period-doubling bifurcation to chaos, period-adding bifurcation with chaos, and period-adding bifurcation with stochastic burstings were identified. The results not only reveal that an experimental neural pacemaker is capable of generating different bifurcation scenarios but also provide a basic framework for bifurcations in neural firing patterns in a two-dimensional parameter space. [ABSTRACT FROM AUTHOR]

In this study, we examine the bifurcation scenarios of a two-dimensional Hindmarsh-Rose type model [Tsuji et al., 2007] with four parameters and simulate some resemblances of neurophysiological features for this model using spike-and-reset conditions. We present possible classifications based on the results of the following assessments: (1) the number and stability of the equilibria are analyzed in detail using a table to demonstrate the matter in which the stability of the equilibrium changes and to determine which two equilibria collapse through the saddle-node bifurcation; (2) the sufficient conditions for an Andronov-Hopf bifurcation and a saddle-node bifurcation are mathematically confirmed; and (3) we elaborately evaluate the sufficient conditions for the Bogdanov-Takens (BT) and Bautin bifurcations. Several numerical simulations for these conditions are also presented. In particular, two types of bistable behaviors are numerically demonstrated: the BT and Bautin bifurcations. Notably, all of the bifurcation curves in the domain of the remaining parameters are similar when the time scale is large. Additionally, to show the potential for a limit cycle, the existence of a trapping region is demonstrated. These results present a variety of diverse behaviors for this model. The results of this study will be helpful in assessing suitable parameters for fitting the resemblances of experimental observations. [ABSTRACT FROM AUTHOR]

In this study, we first present a modeling mechanism for the loss of neurons in limbic brain regions (epileptogenic focus) that could cause epileptic seizures by spreading the pathological dynamics from the focal to healthy brain regions. Prior work has shown that Cellular Automata (CAs) are very effective in simulating physical systems and solving scientific problems by capturing essential global features of the systems resulting from the collective effect of simple system components that interact locally. Nontrivial CAs are obtained whenever the dependence on the values at each CA site is nonlinear. Consequently, in this study, we show that brain activity in a healthy and epileptic state can be simulated by CA long-range interactions. Results from analysis of CA simulation data, as well as real electroencephalographic (EEG) data clearly show the efficiency of the proposed CA algorithm for simulation of the transition to an epileptic state. The results are in agreement with ones from previous studies about the existence of high-dimensional stochastic behavior during the healthy state and low-dimensional chaotic behavior during the epileptic state. The correspondence of the CA simulation results with the ones from real EEG data analysis implies that the spatiotemporal chaotic dynamics of the epileptic brain are similar to observed nonequilibrium phase transition processes in spatially distributed complex systems. [ABSTRACT FROM AUTHOR]

Vertical dynamic properties of the ŠKODA 21 Tr low-floor trolleybus were investigated on an artificial test track when driving with a real vehicle and when simulating driving with a multibody model on a virtual test track. Driving on the artificial test track was aimed at determining the vertical dynamic properties of the real trolleybus, and on such basis, the computer trolleybus models were verified. Time histories and extreme values of the relative deflections of air springs are monitored. The influence of the tire radial characteristics is determined on the basis of measurements on contact surfaces of different shapes that are evaluated. [ABSTRACT FROM AUTHOR]

When nonlinearity is added to an infinite system with purely discrete linear spectrum, Anderson modes become coupled with one another by terms of higher order than linear, allowing energy exchange between them. It is generally believed, on the basis of numerical simulations in such systems, that any initial wave-packet with finite energy spreads down chaotically to zero amplitude with second moment diverging as a power law of time, slower than standard diffusion (subdiffusion). We present results which suggest that the interpretation of spreading cannot be described as initially believed and that new questions arise and still remain opened. We show that an initially localized wave-packet with finite norm may generate two kinds of trajectories both obtained with nonvanishing probability. The first kind consists of KAM trajectories which are recurrent and do not spread. Empirical investigations suggest that KAM theory may still hold in infinite systems under two conditions: (1) the linearized spectrum is purely discrete, (2) the considered solutions are square summable and not too large in amplitude. We check numerically that in appropriate regions of the parameter space, indeed many initial conditions can be found with finite probability that generate (nonspreading) infinite dimension tori (almost periodic solutions) in a fat Cantor set in (projected) phase space. The second kind consists of trajectories which look initially chaotic and often spread over long times. We first rigorously prove that initial chaos does not necessarily imply complete spreading e.g. for large norm initial wave-packet. Otherwise, in some modified models, no spreading at all is proven to be possible, despite the presence of initial chaos in contradiction with early beliefs. The nature of the limit state is still unknown. However, we attempt to present empirical arguments suggesting that if a trajectory starts chaotically spreading, there will necessarily exist (generally large) critical spreading distances that depend on the disorder realization where the trajectory will be sticking to a dense set of KAM tori. This effect should induce drastic slowing down of the spreading which could be viewed as "inverse Arnold diffusion" since the trajectory approaches KAM tori regions instead of leaving them. We suggest that this effect should self-organize the chaotic behavior and that at long time, the wave-packet might not be spread down to zero, but could have a limit profile with marginal chaos (with singular continuous spectrum), despite a long spatial tail. Further analytical and numerical investigations are required. [ABSTRACT FROM AUTHOR]

Some observations are made on a class of one-predator, two-prey models via numerical analysis. The simulations are performed with the aid of an adaptive grid method for constructing bifurcation diagrams and cell-to-cell mapping for global analysis. A two-dimensional bifurcation diagram is constructed to show that regions of coexistence of all three species, which imply the balance of competitive and predatory forces, are surrounded by regions of extinction of one or two species. Two or three coexisting attractors which may have a chaotic member are found in some regions of the bifurcation diagram. Their separatrices are computed to show the domains of attraction. The bifurcation diagram also contains codimension-two bifurcation points including Bogdanov-Takens, Gavrilov-Guckenheimer, and Bautin bifurcations. The dynamics in the vicinity of these codimension-two bifurcation points are discussed. Some global bifurcations including homoclinic and heteroclinic bifurcations are investigated. They can account for the disappearance of chaotic attractors and limit cycles. Bifurcations of limit cycles such as transcritical and saddle-node bifurcations are also studied in this work. Finally, some relevant calculations of Lyapunov exponents and power spectra are included to support the chaotic properties. [ABSTRACT FROM AUTHOR]

The stabilization of nonlinear systems that exhibit chaotic behavior is presented using notch-filter output feedback control. The effect of constant disturbance input and/or parametric uncertainty on the systems' performance is studied for a class of nonlinear systems where bifurcation analysis is used to illustrate the period-doubling route to chaos. The motivation for using the notch-filter in the feedback is to selectively damp-out portions of the closed-loop power spectrum, thus truncating period-doubling. Double-notch-filter feedback is introduced as a regulation scheme to bring the chaotic system to a steady state. The effect of using the fixed-parameters feedback on the equilibrium points is carefully studied, and a robust numerical parameter-tuning method is presented. The efficiency of this method is verified via simulations applied to a third-order uncertain nonlinear system that has typical applications in power generation and voltage control. A comparative study with a model-based recursive backstepping controller is carried out to highlight the advantages and limitations of the proposed control system. [ABSTRACT FROM AUTHOR]

Nonlinear dynamics of a real plane and periodically forced triple pendulum is investigated experimentally and numerically. Mathematical modeling includes details, taking into account some characteristic features (for example, real characteristics of joints built by the use of roller bearings) as well as some imperfections (asymmetry of the forcing) of the real system. Parameters of the model are obtained by a combination of the estimation from experimental data and direct measurements of the system's geometric and physical parameters. A few versions of the model of resistance in the joints are tested in the identification process. Good agreement between both numerical simulation results and experimental measurements have been obtained and presented. Some novel features of our real system chaotic dynamics have also been reported, and a novel approach of the rolling bearings friction modeling is proposed, among other. [ABSTRACT FROM AUTHOR]

A synchronized neural network model with delays is considered. The bifurcations arising from the zero root of the corresponding characteristic equation have been studied by employing the center manifold theorem, normal form method and bifurcation theory. It is shown that the system may exhibit transcritical/pitchfork bifurcation, or Bogdanov–Takens bifurcation. Some numerical simulation examples are given to justify the theoretical results. [ABSTRACT FROM AUTHOR]

A sliding mode control technique is introduced for generalized fractional chaotic systems. These systems are governed by a set of fractional differential equations of incommensurate orders. The proposed design method relies on the fact that the stability region of a fractional system contains the stability region of its underlying integer-order model. A sliding mode controller designed for an equivalent integer-order chaotic system is used to stabilize all its corresponding fractional chaotic systems. The design technique is demonstrated using two generalized fractional chaotic models; a chaotic oscillator and the Chen system. The effect of the total fractional order is investigated with respect to the controller effort and the convergence rate of the system response to the origin. Numerical simulations validate the main results of this work. [ABSTRACT FROM AUTHOR]