An Integer-Order Memristive System with Two- to Four-Scroll Chaotic Attractors and Its Fractional-Order Version with a Coexisting Chaotic Attractor

Abstract EN

First, based on a linear passive capacitor C, a linear passive inductor L, an active-charge-controlled memristor, and a fourth-degree polynomial function determined by charge, an integer-order memristive system is suggested.

The proposed integer-order memristive system can generate two-scroll, three-scroll, and four-scroll chaotic attractors.

The complex dynamics behaviors are investigated numerically.

The Lyapunov exponent spectrum with respect to linear passive inductor L and the two-scroll, three-scroll, and four-scroll chaotic attractors are yielded by numerical calculation.

Second, based on the integer-order memristive chaotic system with a four-scroll attractor, a fractional-order version memristive system is suggested.

The complex dynamics behaviors of its fractional-order version are studied numerically.

The largest Lyapunov exponent spectrum with respect to fractional-order p is yielded.

The coexisting two kinds of three-scroll chaotic attractors and the coexisting three-scroll and four-scroll chaotic attractors can be found in its fractional-order version.