Dynamics of Minimal Networks of Limit Cycle Oscillators

Abstract

The framework of mutually coupled oscillators on a network has served as a convenient tool for investigating the impact of various parameters on the dynamics of real-world systems. Compared to large networks of oscillators, minimal networks are more susceptible to changes in coupling parameters, the number of oscillators, and network topologies. In this study, we systematically explore the influence of these parameters on the dynamics of a minimal network comprising Stuart-Landau oscillators coupled with a distance-dependent time delay. We examine three network topologies: ring, chain, and star. Specifically, for ring networks, we study the effects of increasing nonlocality from local to global coupling on the overall dynamics of the system. Our findings reveal the existence of various synchronized states, including splay and cluster states, a partially synchronized state such as chimeric quasiperiodicity, and an oscillation quenching state such as amplitude death in these networks. Moreover, through an analysis of long-lived transients, we discover novel amplitude-modulated states within ring networks. Interestingly, we observe that increasing nonlocality diminishes the influence of the number of oscillators on the overall behavior in these networks. Furthermore, we note that chain networks, unlike ring networks, do not exhibit perfect synchrony among the coupled oscillators. In contrast, star networks demonstrate greater stability and are unaffected by the number of oscillators within the network. The insights from this study deepen our understanding of the dynamics of minimal networks and have implications for various fields, ranging from biology to engineering.

14 pages, 11 figures

References in corpus (10)

• Synchronization in complex networks
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Remote synchronization reveals network symmetries and functional modules
• Weak chimeras in minimal networks of coupled phase oscillators
• Engineering reaction-diffusion networks with properties of neural tissue
• Experimental investigation on the susceptibility of minimal networks to a change in topology and number of oscillators
• Generalized splay states in phase oscillator networks
• Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions
• Emergence of complex structures from nonlinear interactions and noise in coevolving networks
• Chaotic Chimera Attractors in a Triangular Network of Identical Oscillators

Cited by in corpus (2)

• Computational Identification and Stuart-Landau Modeling of Collective Dynamical Behaviors of Octuple Laminar Diffusion Flame Oscillators
• Dimensionality Reduction and Dynamical Mode Recognition of Circular Arrays of Flame Oscillators Using Deep Neural Network