Synchronization and multistability in the coupled neurons with propagation and processing delays
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ORIGINAL PAPER
Synchronization and multistability in the coupled neurons with propagation and processing delays Chenggui Yao
Received: 16 March 2020 / Accepted: 25 August 2020 © Springer Nature B.V. 2020
Abstract The dynamics of spiking and bursting activities have attracted interest from scientists due to their significance in the brain and neural systems. In this work, the effects of processing delay, specifically the time delay in coupling, on the dynamical behaviors of the coupled Hindmarsh–Rose neurons with resting state are investigated. The results reveal that the processing delay can induce rich spiking patterns, such as anti-phase synchronous spiking, in-phase synchronous periodic bursting, anti-phase synchronous periodic bursting and anti-phase synchronous chaotic bursting, and maintained the bistability and tristability of different spiking patterns. This emphasizes that the processing delay-induced spiking patterns might not be observed in the diffusively coupled neurons with resting state with and without propagation delay. The results can help deepen the knowledge on neural synchronization and information processing in the neuronal network and brain. Keywords Neuronal dynamics · Spiking patterns · Time delay · Electrical synapse
C. Yao (B) College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing 314000, China e-mail: [email protected]
1 Introduction Electrical activities are of great significance for gaining new insight into the information processing in the brain and neuronal system [1,2]. Multistability or bistability with spiking patterns, one of the important electrical activities, is characterized by the coexistence of multiple attractors and is widely distributed in the nervous system [3–5]. Many works have revealed that a plethora of multistability states can coexist in a single neuron and the neuronal networks [6–9]. The bistable states with coexistence of quiescent–spiking or spiking– bursting [10] and synchronization–asynchronization or in-phase and anti-phase firing patterns were usually observed [11–13]. In fact, bistability is also common in the brain. For example, the bistable perception can be observed when the ambiguous sensory inputs are reached [14,15]. Different stimuli can induce a switch between these states, thus reflecting different brain functions [16–18] and physiological diseases such as Parkinson’ s disease and epilepsy [19,20]. The electrical activities of neuronal system are related closely associated with the normal brain function. It is generally believed that the bursting behavior of neurons in the neuronal systems can play significant roles in epileptic seizures and spreading depression, which refer to the physiological diseases induced by the abnormal change of ion concentrations [21–27]. To deal with the problem of multistability, the bursting oscillation and syn-
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C. Yao
chronization in neural networks are of special prime importance [28,29]. The electrical activity for both synchronization and desynchronization is o
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