Synchronization in the two time-scale multiplex network with symplectic interactions

Abstract

Mounting experimental evidence suggests a significant role for glial cells, particularly astrocytes, in shaping neuronal activity in both cell cultures and the brain, driving interest in exploring multi-component network dynamics [1]. These systems are modeled at varying levels of physiological detail, ranging from the Hodgkin-Huxley and Ullah models for neurons and astrocytes, respectively, to simple integrate-and-fire models or phase oscillators. Multiplex networks are commonly used to model generic dynamical phenomena, with an emphasis on network connectivity effects rather than the complexity of an individual cell’s behavior. This model is particularly advantageous due to its use of a two-layer network structure [2]. This structure accurately describes neural connectivity through the long-range random coupling, while glial cells interact locally through the diffusion of mediatory molecules. Furthermore, the oscillatory timescales between neural and glial cells differ by at least one order of magnitude. In this context, the analysis of synchronization is a focal point as it is a crucial process that underpins information processing, decision making, and movement control in living neural systems [3]. Network topology is known to be essential, where all-to-all coupling and random Erdos–Renyi connectivity support the second-order phase transition to global phase coherence. In contrast, regular local coupling such as a 2D lattice only permits frequency and phase locking. Additionally, symplectic networks are capable of demonstrating a first-order phase transition, which is commonly referred to as “explosive” synchronization [4]. Recently, studies have shown that combining model neural (random) and glial (regular lattice) oscillatory layers can lead to a variety of outcomes [5]. Specifically, this combination was found to induce a second-order phase transition in the regular glial layer. In addition, synchronization in both layers may be preceded by desynchronization as the coupling between the layers becomes stronger. Here we investigate synchronization in the multiplex neural-glial network, where the neural layer is symplectic and contains triadic interactions. We demonstrate that symplectic coupling in the neural layer can induce the first order transition in the regular (glial) layer. Additionally, we show that such a transition can be induced by strengthening the glial and interlayer coupling, even if the symplectic neural layer alone is below the synchronization threshold. Desynchronization in the neuronal layer, resulting from the moderated coupling to the glial layer, never occurs abruptly.