Chimera States On Neural Networks

The human brain is one of the most complicated systems in nature.There are approximately 10¹¹neurons in the human brain.These neurons connect to each other through approximately 10¹⁴synapses to form a complex network of brain structures.The human brain network is the physiological basis of the brain for information pro-cessing and cognitive expression.These structural characteristics are closely related to the functions of the human brain.In neuroscience,synchronous behavior of neurons plays an important role in cognitive processes such as learning and memory,and ab-normal synchronization is closely related to neurological diseases such as synchronous abnormalities.The enhancement of synchronization leads to epilepsy,and the loss of synchronization can lead to schizophrenia and other diseases.More than a decade ago,a bizarre synchronization phenomenon was observed in the symmetry-coupled oscillatory system,namely the co-existence of synchronous and non-synchronous regions,which was later named chimera state.Since then,the chimera state has attracted the interest of many researchers.The existence of chimera states has been extended from the original phase oscillator to various chaotic oscilla-tory systems.Potential applications of chimera states include bump states in working memory and the phenomenon of unihemispheric sleep observed in birds and dolphins,etc.A recent study by the team of Brown University found that human sleep also has differences between the left and right hemispheres,suggesting that the human brain also has some characteristics similar to that of unihemispheric sleep.Therefore,it is very meaningful to study the chimera state of oscillators on neural networks.This article mainly studies the chimera states on neural networks.The main re-sults are as follows:1.We have constructed an adaptive network model of two subsystems to study the robustness of chimera states and the relationship between synchronization attractor and chimera state attractor.The results of our study show that in the case of symmetric coupling,two clusters can easily goto different final states,thus showing the robust-ness of the chimera state.We study two kinds of asymmetric couplings.The results show that the probability of two clusters to synchronous attractors is limited,that is,it partially destroys the robustness of chimera states.Whether it is an asymmetric intercluster coupling or an asymmetric intracluster coupling,we can reveal that they exhibit the diversity of the patterns of synchronous attractors in the phase diagram of the initial condition.In addition,in order to explain the mechanism for the chimera state to synchrony transition,we performed a bifurcation analysis of the model.2.For the first time,we studied the influence of electromagnetic induction on chimera state and extended the original two-variable FitzHugh-Nagumo model into a three-variable model.In our model,when considering only time-delayed coupling,the chimera state can be observed by choosing the appropriate time delayand coupling strength(8,indicating that time delay is the necessary conditions for the generation of chimera states.When considering only the electromagnetic induction effect,we find that chimera state is affected by the dynamic behavior of a single neuron.When electromagnetic induction and time delay are combined,we find that their cooperation will lead to richer and more robust singularity.3.Most of the current studies on chimera states are focused on one-dimensional ring networks and consider phase models and non-phase models.In addition,some studies have extended the studies of chimera states to two-dimensional networks but only in phase models.We extended the study of chimera state to a two-dimensional neural network and observed new chimera patterns such as grid chimera state and multi-cluster chimera state etc.We propose a new method to change the coupling structure,and find that the deletion of some coupled connections according to certain rules will lead to the diversity of chimera states.4.FitzHugh-Nagumo neurons oscillators and Kuramoto oscillators are used to de-scribe the node's dynamic behavior on the human cortical network.Our study found that when the time delayand coupling strength(8 are appropriately chosen,the dis-order state,multi-cluster chimera state,and synchronous state can be observed in both models.The Ott-Antonsen dimensionality reduction theory was used to theoretical-ly analyze the Kuramoto phase oscillator model.The theoretical solution is in good agreement with the numerical simulation results.