<p>Multistable dynamical systems are characterized by their ability to exhibit multiple coexisting attractors, dependent on the initial conditions. Synchronizing coupled multistable systems is particularly challenging because the synchronization manifold is highly sensitive to initial conditions and coupling parameters, often making it difficult to determine. In this study, we explore the use of a pinning controller to achieve synchronization within a network of bistable Rössler systems, with coexistence of a periodic and a chaotic attractor. We analyze the synchronization of coupled Rössler systems and their manifold under the influence of either a periodic or chaotic pinning controller, using various initial conditions. Our findings reveal that a periodic controller achieves synchronization at lower coupling strengths compared to a chaotic controller, even when initial conditions originate within the chaotic basin of attraction. Additionally, the network’s behavior is evaluated with both periodic and chaotic pinning controllers to delineate each controller’s synchronization region and identify the dominant synchronization manifold. Results indicate that the periodic attractor’s synchronization region is broader than that of the chaotic attractor. Furthermore, as the feedback gain of the periodic controller increases, the chaotic attractor is suppressed regardless of the chaotic feedback gain, whereas periodic synchronization remains influenced by both feedback gains.</p>

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Comparative analysis of periodic and chaotic pinning control for synchronization in coupled multistable systems

  • Tengfei Lei,
  • Haiyan Fu,
  • Hongyan Zang,
  • Lili Huang

摘要

Multistable dynamical systems are characterized by their ability to exhibit multiple coexisting attractors, dependent on the initial conditions. Synchronizing coupled multistable systems is particularly challenging because the synchronization manifold is highly sensitive to initial conditions and coupling parameters, often making it difficult to determine. In this study, we explore the use of a pinning controller to achieve synchronization within a network of bistable Rössler systems, with coexistence of a periodic and a chaotic attractor. We analyze the synchronization of coupled Rössler systems and their manifold under the influence of either a periodic or chaotic pinning controller, using various initial conditions. Our findings reveal that a periodic controller achieves synchronization at lower coupling strengths compared to a chaotic controller, even when initial conditions originate within the chaotic basin of attraction. Additionally, the network’s behavior is evaluated with both periodic and chaotic pinning controllers to delineate each controller’s synchronization region and identify the dominant synchronization manifold. Results indicate that the periodic attractor’s synchronization region is broader than that of the chaotic attractor. Furthermore, as the feedback gain of the periodic controller increases, the chaotic attractor is suppressed regardless of the chaotic feedback gain, whereas periodic synchronization remains influenced by both feedback gains.