Deterministic coherence resonance analysis of coupled chaotic oscillators: fractional approach

• Published in: Chaos, solitons and fractals solitons and fractals, 2022-04, Vol.157, p.111919, Article 111919
• Main Authors: Gilardi-Velázquez, H.E., Echenausía-Monroy, J.L., Jaimes-Reátegui, R., García-López, J.H., Campos, Eric, Huerta-Cuellar, G.
• Format: Article
• Language: English
• Subjects: Chaotic systems; Coupled systems; Deterministic resonance; Fractional-order systems; Nonlinear dynamics
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2022.111919

•Deterministic coherence resonance phenomenon is studied from fractional calculus analysis and compared with the results of integer order.•Changes of the frequency of coupled systems are shown.•Stability analysis of systems under variation of natural frequency are studied.•Changes of response frequency versus natural frequency under variation of fractional order are shown. Recently, the stabilization of chaos by chaos has attracted the attention of researchers. A small deviation between the natural frequencies of unidirectionally coupled chaotic oscillators can cause the emerge of a coherence resonance in the slave oscillator for a given coupling strength. In this work, we investigate the phenomenon of coherence resonance for a coupled Rössler system under the influence of fractional operators in the frequency response of the slave oscillator. Based on the analysis of the fractional Rössler system, we determine a range of fractional orders in which the system retains its instability, and an analysis of the frequency response of the system to changes in natural frequency is developed. Finally, the frequency response of the slave system to changes in the fractional derivative order, the natural frequency of the master system, and the coupling strength is analyzed, and how these changes promote the occurrence of coherence resonance is examined.