In this case-study, we examine the effects of linear control on continuous dynamical systems that exhibit chaotic behavior using the symbolic computer algebra system Mathematica. Stabilizing (or controlling) higher-dimensional chaotic dynamical systems is generally a difficult problem, Musielak and Musielak, [1]. We numerically illustrate that sometimes elementary approaches can yield the desir...

In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical si...

Generic dynamical systems are characterized by the coexistence of chaotic regions and regular structures, and typical trajectories present regular segments, due to sticking to the ordered component of the phase space, separated by erratic behavior, due to wanderings in the chaotic sea. Though ubiquitous, this mixed behavior still involves hard theoretical problems, as present theories are tailo...

in this paper, we discuss the dynamical properties of a chemical reactor model including lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos. we study the synchronization of chemical reactors model via sliding mode control scheme. the stability of proposed method is proved by barbalate’s lemma. numeri...

The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expect...

Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through t...

The experimental study of a secure chaotic synchronized communication system is presented. The synchronization between two digital chaotic oscillators, serving as a transmitter-receiver scheme, is studied. The oscillators exhibit rich chaotic behavior and are unidirectionally coupled, forming a master-slave topology. Both the input information signal and the transmitted chaotic signal are digit...

This paper presents a procedure to transform a chaotic logistic map into a continuous-time delay chaotic system by using sampled-data representation of continuous-time models. Because of this, the chaotic behavior of the resultant scheme is easy to proofread. A numerical illustration is also realized by utilizing Matlab/Simulink, where the new resultant chaotic attractor is shown.

We investigate the origin of diffusion in non-chaotic systems. As an example, we consider 1D map models whose slope is everywhere 1 (therefore the Lyapunov exponent is zero) but with random quenched discontinuities and quasi-periodic forcing. The models are constructed as non-chaotic approximations of chaotic maps showing deterministic diffusion, and represent one-dimensional versions of a Lore...

Chaotic iterations, a tool formerly used in distributed computing, has recently revealed various interesting properties of disorder leading to its use in the computer science security field. In this paper, a comprehensive study of its topological behavior is proposed. It is stated that, in addition to being chaotic as defined in the Devaney’s formulation, this tool possesses the property of top...