Analysis and electronic circuit implementation of an integer- and fractional-order four-dimensional chaotic system with offset boosting and hidden attractors

• Published in: The European physical journal. ST, Special topics Vol. 229; no. 6-7; pp. 1211 - 1230
• Main Authors: Tamba, Victor Kamdoum, Kom, Guillaume Honoré, Kingni, Sifeu Takougang, Mboupda Pone, Justin Roger, Fotsin, Hilaire Bertrand
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-03-2020; Springer Nature B.V
• Subjects: Atomic; Bifurcations; Chaos theory; Circuits; Classical and Continuum Physics; Computer simulation; Condensed Matter Physics; Electronic circuits; Integers; Materials Science; Mathematical models; Measurement Science and Instrumentation; Molecular; Nonlinear systems; Numerical methods; Optical and Plasma Physics; Physics; Physics and Astronomy; Regular Article; Routh-Hurwitz criterion; Special Chaotic Systems; Stability analysis
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2020-900169-1

In this paper, an integer- and fractional-order form of a four-dimensional (4-D) chaotic system with hidden attractors is investigated using theoretical/numerical and analogue methods. The system is constructed not through the extension of a three-dimensional existing nonlinear system as in current approaches, but by modifying the well-known two-dimensional Lotka-Volterra system. The equilibrium point of the integer-order system is determined and its stability analysis is studied using Routh-Hurwitz criterion. When the selected bifurcation parameter is varied, the system exhibits various dynamical behaviors and features including intermittency route to chaos, chaotic bursting oscillations and offset boosting. Moreover, the fractional-order form of the system is examined through bifurcation analysis. It is revealed that chaotic behaviors still exist in the system with order less than four. To validate the numerical approaches, a corresponding electronic circuit for the model in its integer and fractional order form is designed and implemented in Orcard-Pspice software. The Pspice results are consistent with those from the numerical simulations.