Abstract
AbstractThis paper presents a control technique capable of driving a harmonically driven nonlinear system between two distinct periodic orbits. A vital component of the method is a temporary dual-frequency driving with tunable driving amplitudes. Theoretical considerations revealed two necessary conditions: one for the frequency ratio of the dual-frequency driving and another one for torsion numbers of the two orbits connected by bifurcation curves in the extended dual-frequency driving parameter space. Although the initial and the final states of the control strategy are single-frequency driven systems with distinct parameter sets (frequencies and driving amplitudes), control of multistability is also possible via additional parameter tuning. The technique is demonstrated on the symmetric Duffing oscillator and the asymmetric Toda oscillator.
Funder
Ministry of Innovation and Technology of Hungary
J́anos Bolyai Research Scholarship of the Hungarian Academy of Sciences
New National Excellence Program of the Ministry of Human Capacities
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
Nvidia
Max Planck Institute for Dynamics and Self-Organization (MPIDS)
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Control and Systems Engineering
Reference92 articles.
1. Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20(2), 130 (1963)
2. Rajagopal, K., Pham, V.T., Alsaadi, F.E., Alsaadi, F.E., Karthikeyan, A., Duraisamy, P.: Multistability and coexisting attractors in a fractional order Coronary artery system. Eur. Phys. J. Spec. Top. 227, 837 (2018)
3. Pati, N.C., Layek, G.C., Pal, N.: Bifurcations and organized structures in a predator-prey model with hunting cooperation. Chaos, Solitons and Fractals 140, 110184 (2020)
4. Hossain, M., Pal, S., Tiwari, P.K., Pal, N.: Bifurcations, chaos, and multistability in a nonautonomous predator-prey model with fear. Chaos 31(12), 123134 (2021)
5. Pati, N.C., Garai, S., Hossain, M., Layek, G.C., Pal, N.: Fear Induced Multistability in a Predator-Prey Model. Int. J. Bifurc. Chaos 31(10), 2150150 (2021)