https://doi.org/10.1140/epjp/s13360-022-02903-4
Regular Article
Effect of amplitude-modulated force on horseshoe dynamics in Briggs–Rauscher chemical system modeled by a new parametric oscillator with asymmetric potential
1
Department of Industrial and Technical Sciences, UNSTIM-Abomey, ENSET-Lokossa, BP 133, Lokossa, Benin
2
National Higher Institute of Industrial Technology, National University of Sciences, Technologies, Engineering and Mathematics of Abomey (UNSTIM), Abomey, Benin
3
Department of Physics, University of Abomey-Calavi, Abomey-Calavi, Benin
Received:
30
December
2021
Accepted:
30
May
2022
Published online:
10
June
2022
In this paper, the effect of amplitude-modulated force on horseshoe dynamics in Briggs–Rauscher chemical system modeled by a nonlinear parametric asymmetric oscillator is investigated analytically and numerically. By applying Melnikov method, the homoclinic bifurcation condition of existence of chaotic motion is derived. The domain where appears the horseshoe chaos decreases when the amplitude-modulated excitation increases. The numerical simulations based on the basin boundaries of attraction confirm the obtained analytical prediction. In addition, it is found that the increase in amplitude-modulated excitation provokes the erosion of the basin of attraction and the decrease of the strangeness of the chaotic attractors. It is also found that the initial conditions affect the fractal geometric shape of the chaotic attractors. The global dynamical changes are numerically examined by evaluating the effect of amplitude-modulated force on the bifurcation diagrams. The obtained results show that the amplitude-modulated excitation induces in the system a rich variety of bifurcation phenomena such as symmetry breaking, symmetry restoring, period-doubling and reverse period-doubling bifurcations, antimonotonicity, intermittency, remerging chaotic band attractors, period-m bubbles, chaos and remarkable routes to chaos. Moreover, the variation of amplitude-modulated excitation has a real impact on the geometry of the chaotic attractors. Further, for large amplitude-modulated excitation, the chaotic motion disappears, and regular behavior takes place in the chemical system. On the other hand, for certain values of the system parameters, the new chemical system displays transient chaos.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
