Study On Chimera Dynamics And Circuit Simulation Of Hindmarsh-Rose Neuronal Networks

Chimera state is a counterintuitive and symmetry-breaking spatiotemporal pattern where coherence and incoherence coexist in systems composed of identically coupled oscillators.Recent studies have shown that chimera state also exists in the nervous system and is related to the evolution and development of neurons and neural information processing.Since the complex structure and large scale of the nervous system,it is necessary to construct neuronal network models to explore the origin,behavioral characteristics and changing laws of chimera states.Moreover,signal transduction and ion exchange in biological neuronal networks can generate complex electromagnetic fields that exhibit memristive properties.So,constructing memristive neuronal network models to study complex neuronal dynamics including chimera states is necessary.Furthermore,using the circuit to reproduce the chimera states will provide reference for the realization of artificial nervous system or “artificial brain”.In this thesis,Hindmarsh-Rose neuronal network models coupled with chemical synapses and memristive synapses are constructed,respectively.The chimera spatiotemporal dynamic behaviors of neuronal networks are explored by numerical simulation,and a simulation circuit is built in Multisim to reproduce the chimera phenomenon of memristive neuronal networks.The main contributions of this thesis are divided into the following three parts:Firstly,a two-layer neuronal network model with chemical synaptic coupling is constructed,and the local,non-local,and global connections of the network are realized,respectively.By varying parameters such as intra-layer and inter-layer synaptic coupling strengths,it is found that different inter-layer interactions and network topologies in multilayer neuronal networks can stimulate the system to produce various types of chimera states and neuronal firing patterns.Particularly,a“coherent wave state” existing in locally and non-locally coupled networks,and an “inter-layer semi-synchronous chimera state” composed of both inter-layer synchronous and asynchronous chimera states are observed.Moreover,the results of numerical simulations show that globally coupled networks are unable to generate traveling chimera states.Then,a locally coupled memristive neuronal network considering excitatory and inhibitory connections is proposed,and various connections such as excitation,inhibition,excitation/inhibition are realized by changing the synaptic coupling strengths.The effects of parameters such as synaptic coupling strengths and memristive coefficients on the network synchronous state are also investigated.The results show that changing the connection modes and memristive coefficients between neurons will make the memristive neuronal network produce abundant spatiotemporal dynamic behaviors.In particular,a novel chimera state and a novel neuronal firing pattern are discovered,which are named “semi-traveling chimera state” and “mixed-amplitude bursting state”,respectively.In addition,the law of multi-head traveling chimera and transient chimera states with parameter changes is also found.Finally,a locally coupled memristive neuronal network circuit is designed and built in the Multisim software.The excitatory,inhibitory,and excitatory/inhibitory connections between neurons are realized by changing the parameters of the circuit elements.Varying the coupling strengths of memristive synapses,the circuit exhibits a variety of dynamic behaviors including chimera states,and the simulation results are consistent with the phenomena of numerical simulations.Furthermore,our results demonstrate the feasibility of reproducing chimera states in real circuits and provide clues for the implementation of neuromorphic hardware.In conclusion,this thesis mainly investigates the spatiotemporal dynamics of chimera states in neuronal networks of coupled Hindmarsh-Rose neurons,which is expected to deepen the understanding of the evolution of neurons in which coherent and incoherent dynamics coexist,and provide useful clues for the realization of artificial nervous system or artificial brain.