A Novel Chaotic System without Equilibrium: Dynamics, Synchronization, and Circuit Realization

Abstract

A few special chaotic systems without unstable equilibrium points have been investigated recently. It is worth noting that these special systems are different from normal chaotic ones because the classical Shilnikov criterion cannot be used to prove chaos of such systems. A novel unusual chaotic system without equilibrium is proposed in this work. We discover dynamical properties as well as the synchronization of the new system. Furthermore, a physical realization of the system without equilibrium is also implemented to illustrate its feasibility.

Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

“…In these last years, hyperchaotic systems have gained the interest of the scientific community and new systems and circuits are proposed [3][4][5][6][7][8]. This great interest can be explained by the aptitude of hyperchaotic systems to generate complex dynamics characterized by more than one positive Lyapunov exponent and attractors deployed in multiple directions.…”

“…The most famous chaotic one is the Jerk system proposed by sprott, in 1994 [12,13], which contains simple nonlinear terms. However, it is well known that most systems contain conventional nonlinear terms like piecewise linear functions [14][15][16][17], integer order polynomials [8,18], sine functions [19], time delayed functions [20], and switching functions [21]. In this framework, fractional-order polynomials could be used to build complex chaotic behaviors and, to the best of our knowledge, they have not been harnessed until now.…”

Analysis of a Chaotic System with Line Equilibrium and Its Application to Secure Communications Using a Descriptor Observer

“…Over the years, chaos synchronization has found applications in many scientific disciplines, including, but not limited to, encryption and secure transmission [2][3][4][5][6][7][8], optics and lasers [9,10], engineering [11] and robotics [12][13][14]. So far, a wide variety of design approaches have been applied for synchronization [2,[15][16][17][18][19][20][21][22][23][24].…”

A New Simple Chaotic Lorenz-Type System and Its Digital Realization Using a TFT Touch-Screen Display Embedded System

“…Since then, many chaotic systems like Lorenz-and their chaotic behavior-have been reported in the literature, for example, [17][18][19][20][21][22][23]. Currently, we can mention some new chaotic systems reported in the literature [24][25][26][27][28][29][30][31][32][33].…”

“…The CVs usually are represented by using OAs [31,34]. For DVs, Matlab or Labview allows simulating the dynamical behaviors of discretized chaotic systems to desirably obtain the less degradation with respect to CVs, and their implementations are reproduced by using ESs as FPGAs [35], DSPs [36], or microcontrollers [37][38][39].…”