Chaotic Behaviors and Coexisting Attractors in a New Nonlinear Dissipative Parametric Chemical Oscillator

• Published in: Complexity (New York, N.Y.) N.Y.), 2022, Vol.2022 (1)
• Main Authors: Kpomahou, Y. J. F., Adomou, A., Adéchinan, J. A., Yamadjako, A. E., Madogni, I. V.
• Format: Article
• Language: English
• Subjects: Algorithms; Attractors (mathematics); Behavior; Bifurcations; Broken symmetry; Bubbles; Chaos theory; Differential equations; Engineering; Investigations; Mathematical models; Parametric amplifiers; Period doubling; Runge-Kutta method; Symmetry
• ISSN: 1076-2787; 1099-0526
• DOI: 10.1155/2022/9350516

In this study, complex dynamics of Briggs–Rauscher reaction system is investigated analytically and numerically. First, the Briggs–Rauscher reaction system is reduced into a new nonlinear parametric oscillator. The Melnikov method is used to derive the condition of the appearance of horseshoe chaos in the cases ω=Ω and ω≠Ω. The performed numerical simulations confirm the obtained analytical predictions. Second, the prediction of coexisting attractors is investigated by solving numerically the new nonlinear parametric ordinary differential equation via the fourth-order Runge–Kutta algorithm. As results, it is found that the new nonlinear chemical system displays various coexisting behaviors of symmetric and asymmetric attractors. In addition, the system presents a rich variety of bifurcations phenomena such as symmetry breaking, symmetry restoring, period doubling, reverse period doubling, period-m bubbles, reverse period-m bubbles, intermittency, and antimonotonicity. On the contrary, emerging chaotic band attractors and period-1, period-3, period-9, and period-m bubbles routes to chaos occur in this system.