Eur. Phys. J. Plus (2019) 134: 444
https://doi.org/10.1140/epjp/i2019-12688-8

Regular Article

Dynamics analysis of a fractional-order delayed SBT memristive chaotic system without equilibrium points

¹ Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei, China
² School of Electronics and Information Engineering, Anhui University, 230601, Hefei, China

^* e-mail: wn_xlb@ahu.edu.cn

Received: 4 March 2019
Accepted: 12 April 2019
Published online: 13 September 2019

Abstract

The SBT memristor is a physical memristor using a Sr0.95Ba0.05TiO3 nanometer film, which is presented with a flux-controlled mathematical model. The integer-order chaotic systems based on SBT memristor have attracted much attention and have been thoroughly discussed. Analysis shows that the fractional-order system is closer to real system. In this paper, a fractional-order delayed SBT memristive chaotic system is proposed. It is worth noting that this fractional-order delayed SBT memristive system can produce chaotic attractors although it has no equilibrium points. A key system parameter is investigated by theoretical analyses and numerical simulations using the modified Adams-Bashforth-Moulton method. The results indicate that the system parameter can significantly affect the dynamic behavior, which can be indicated by the bifurcation diagrams, the Max Lyapunov exponent (MLE) diagram, the time domain waveform, the phase portraits and the power spectrum of the oscillator. All research can lay a significant theoretical foundation for the physical realization of chaotic circuits.