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Multistability Analysis and Function Projective Synchronization in Relay Coupled Oscillators

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  • Ahmad Taher Azar
  • Ngo Mouelas Adele
  • Kammogne Soup Tewa Alain
  • Romanic Kengne
  • Fotsin Hilaire Bertrand

Abstract

Regions of stability phases discovered in a general class of Genesio−Tesi chaotic oscillators are proposed. In a relatively large region of two-parameter space, the system has coexisting point attractors and limit cycles. The variation of two parameters is used to characterize the multistability by plotting the isospike diagrams for two nonsymmetric initial conditions. The parameters window in which the jerk system exhibits the unusual and striking feature of multiple attractors (e.g., coexistence of six disconnected periodic chaotic attractors and three-point attraction) is investigated. The second aspect of this study presents the synchronization of systems that act as mediators between two dynamical units that, in turn, show function projective synchronization (FPS) with each other. These are the so-called relay systems. In a wide range of operating parameters; this setup leads to synchronization between the outer circuits, while the relaying element remains unsynchronized. The results show that the coupled systems can achieve function projective synchronization in a determined time despite the unpredictability of the scaling function. In the coupling path, the outer dynamical systems show finite-time synchronization of their outputs, that is, displaying the same dynamics at exactly the same moment. Further, this effect is rather general and it has a wide range of applications where sustained oscillations should be retained for proper functioning of the systems.

Suggested Citation

  • Ahmad Taher Azar & Ngo Mouelas Adele & Kammogne Soup Tewa Alain & Romanic Kengne & Fotsin Hilaire Bertrand, 2018. "Multistability Analysis and Function Projective Synchronization in Relay Coupled Oscillators," Complexity, Hindawi, vol. 2018, pages 1-12, January.
    • Handle: RePEc:hin:complx:3286070
    DOI: 10.1155/2018/3286070
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    References listed on IDEAS

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    1. Bao, B.C. & Bao, H. & Wang, N. & Chen, M. & Xu, Q., 2017. "Hidden extreme multistability in memristive hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 102-111.
    2. Freire, Joana G. & Gallas, Jason A.C., 2014. "Cyclic organization of stable periodic and chaotic pulsations in Hartley’s oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 129-134.
    3. Oliveira, Diego F.M. & Leonel, Edson D., 2013. "Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1762-1769.
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    1. Wu, H.G. & Ye, Y. & Bao, B.C. & Chen, M. & Xu, Q., 2019. "Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 178-185.

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