Simplest 3d Continuous-Time Quadratic Systems as Candidates for Generating Multiscroll Chaotic Attractors

Abstract

In this paper, we present a simple approach to produce n-scroll chaotic attractors in 3D quadratic continuous time systems. The method of analysis is based on the number of equilibrium points. Some numerical results are also given and discussed.

Periodic Orbits Bifurcating from a Nonisolated Zero–Hopf Equilibrium of Three-Dimensional Differential Systems Revisited

“…In section 3 we shall apply Theorem 1 to study three polynomial differential systems of degree two that cannot be studied using Llibre & Xiao [2014, Theorem 2.4]. More precisely these three polynomial differential systems are system (11) proposed by Li [2008], system (12) provided by Pan et al [2010] and system (10) proposed by Elhadj & Sprott [2013]. For certain coefficients values all these systems present n-scroll chaotic attractors.…”

“…This type of system has several real word applications, for instance in engineering and secure communication. Elhadj & Sprott [2013] have shown that the simplest family of systems displaying n-scroll chaotic attractors is given by the quadratic polynomial differential systemẋ…”

New technique to quantify chaotic dynamics based on differences between semi-implicit integration schemes

“…Over the past decades, the number of publications considering new chaotic systems and their applications has increased significantly [1][2][3][4][5][6] . In that regard, J.C. Sprott in [7] proposed a standard that establishes the requirements for research published in nonlinear dynamics.…”

Design and implementation of grid multi-scroll fractional-order chaotic attractors

“…13 Nowadays, there are many methods to design and realize MSCA in the classical differential systems. [14][15][16] In the last decades, fractional calculus have gained considerable research attention for its more advantages than classical integer-order ones in describing memory and hereditary properties of many materials and processes. [17][18][19][20][21][22][23] It was recognized that many fractional-order (FO) nonlinear differential systems, including the FO Duffing oscillator, 24 the FO Chua circuit, 25 or the so-called FO R€ ossler, 26 FO Chen,27 FO Lorenz, 28 FO L€ u, 29 and FO Liu systems, 30 exhibit complex bifurcations and chaotic phenomena.…”