Chaos in fractional system with extreme events

Abstract

Understanding extreme events attracts scientists due to substantial impacts. In this work, we study the emergence of extreme events in a fractional system derived from a Liénard-type oscillator. The effect of fractional-order derivative on the extreme events has been investigated for both commensurate and incommensurate fractional orders. Especially, such a system displays multistability and coexistence of multiple extreme events.

A Conservative Hyperchaostic Memristor System with Extreme Multistability

“…In 1975, the mathematically precise description of chaos was given by Li and Yorke [19]. Later the chaos from different senses, such as Devaney [20], symbolic dynamics [21], fractional-order [22], and topological horseshoe [23] were proposed and analyzed. Based on chaotic theory, chaotic systems have one positive Lyapunov exponent, and hyperchaotic systems have two or more positive Lyapunov exponents.…”

Circuit application of chaotic systems: modeling, dynamical analysis and control

“…Moreover several papers address the dynamical analysis and control of special chaotic systems [33][34][35][36][37]. Authors in paper [33] give a class of simplest symmetric chaotic flows with different equilibria and investigate the chaos synchronization of the systems for revealing the collective behaviors of networks of these systems by analyzing the corresponding master stability function.…”

“…The design of pseudo-random number generator illustrates the effectiveness of engineering application of the system. Authors in paper [35] study the multistability and chaos of fractional-order oscillator with extreme events. Authors in paper [36] consider the complex generalized synchronization control problem of complex-variable chaotic systems and establish the synchronization conditions by using Lyapunov stability theory.…”