Emergence of chimeralike oscillation modes in excitable complex networks with preferentially cutting–rewiring operation

Abstract

In this paper, the preferentially cutting–rewiring operation (PCRO) consisting of the cutting procedure and the rewiring procedure is proposed and is applied on an excitable Erdös–Rényi random network (EERRN), by which the structure of the initially homogeneous network changes dramatically, and lots of common leaves (CLs) are formed between the two hubs. Subsequently, besides the single-mode oscillations that can be usually observed in homogeneous excitable systems, a new kind of multi-mode oscillations composed of synchronous and asynchronous parts can self-organize to emerge, which are similar to the coherent and incoherent clusters in traditional chimera states and are consequently named as the chimeralike oscillation modes (CLOMs). Importantly, by utilizing the dominant phase-advanced driving method, both the mechanisms for the formation and the emergence of CLOMs in EERRNs with PCRO are well explained, among which the CL is exposed to play a key role in forming the CLOMs. Furthermore, the PCRO-induced CLOM phenomena can also be observed in other paradigmatic network models or with other paradigmatic excitable dynamics, which definitely confirms that the PCRO is an universal method in inducing the CLOMs in excitable complex networks. Our contributions may shed lights on a new perspective of the emergence of CLOMs in complex systems and would have great impacts in related fields.

A statistical analysis method for probability distributions in Erdös–Rényi random networks with preferential cutting–rewiring operation

“…In the PCRO rewiring procedure, we reconnect these isolated nodes to the hubs satisfying the corresponding preferential constraint, which can be roughly regarded as the specialized regulatory centers (i.e., the hub regions) in brain networks to perform global physiological functions among the whole brain system. Furthermore, in a recent contribution ( Qian et al, 2024b ), the PCRO-induced oscillation mode transition from the originally single-mode oscillations to the newly multi-mode oscillations has been confirmed to emerge among the preferentially operated nodes (i.e., the integrated local modules), which we think is beneficial for understanding the complicated global multimodal physiological functions in integrated structural and functional brain networks. More importantly, the probability distributions of the three different types of isolated nodes formed in the PCRO are derived according to the statistical analysis method proposed in this article, based on which the probability distribution of the preferentially operated common leaves is acquired explicitly.…”