Eur. Phys. J. Special Topics 228, 195–207 (2019)
https://doi.org/10.1140/epjst/e2019-800166-y

Regular Article

Complex dynamics and multiple coexisting attractors in a fractional-order microscopic chemical system

¹ School of Physics and Electronics, Central South University, Changsha 410083, P.R. China
² Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
³ Malaysia-Italy Centre of Excellence for Mathematical Science, Universiti Putra Malaysia, Serdang, Malaysia

^a e-mail: santoban@gmail.com

Received: 4 October 2018
Received in final form: 21 February 2019
Published online: 30 May 2019

Abstract

In this paper, we proposed a fractional-order microscopic chaotic system, derived from a set of microscopic chemical reactions. The dynamical properties of the proposed model have been investigated through Lyapunov characteristic exponents, bifurcation, spectral entropy and C₀ complexity algorithm. The results show that the system has rich dynamics in derivative order and the system parameter. In addition, multiple coexisting attractors are found in the system by selecting appropriate initial values. Complexity measuring algorithms are developed as an effective tool for the detection of such attractors. The results are effective for the dynamical randomness in the collisional motion of atoms and molecules in fluids to produce the deterministic chemical chaos, even in fractional order.