# Effects of Synaptic Pruning on Phase Synchronization in Chimera States of Neural Network
## 1 Introduction  
The coexistence of synchronization and desynchronization in complex systems has been attracting attention for a long time in many fields, including neuroscience, physics, cybernetics, and mechanics. Researchers have already noticed that changes in the topology and coupling of the complex system can affect the spatial and temporal distribution of synchronized regions. Though there are some techniques that can be used to control the synchronized regions in complex systems, these techniques are still facing many limitations both in theory and applications. Neurons are coupled with each other as a network through synaptic connections. In their interaction, most neurons in the network are periodically activated and inhibited, which can be shown from the oscillation of extracellular potential. The frequency of neuron oscillations can vary from less than one hertz to more than one hundred hertz. The phase of a neuron is used to describe the neuron's state, and phase synchronization refers to a large number of neurons discharging at the same time. As one of the most fundamental neural network mechanisms, phase synchronization benefits neural communication and neural plasticity. Therefore, it is involved in many cognitive functions, including the formation of both working memory and long-term memory [1; 2; 3]. One of the fundamental phenomena in brain development is synaptic pruning, which refers to the reduction in the amount and density of synapses that occur between childhood and sexual maturation. As a brain matures, half of the synapses are pruned. This process is largely determined by the environment and highly related to the study behavior of the brain [4; 5; 6]. It is shown in many studies that synaptic pruning affects the performance of phase synchronization in many diseases. The brains of people with Alzheimer's show desynchronization electrical activity, while synaptic pruning is also dysfunctional [8]. The brains of people with Autism Spectrum Disorder have auditory neural synchronization abnormalities, while synaptic pruning is lacking in the auditory cortex [9]. These studies show that lacking synaptic pruning may make neural synchronization abnormal and finally cause diseases. The dynamic behaviors of coupled oscillators, especially synchronization, have attracted great attention due to their application in many subjects. Chimera states arephenomena characterized by the coexistence of coherent domains (periodic in-phase oscillations) and incoherent domains (characterized by a chaotic behavior in time and space) in the coupling system of identical oscillators [10; 11]. This phenomenon occurs in coupled FHN neural oscillators [12; 13] and relates to many brain functions and diseases [14], including neural bump states [15], uni-hemispheric sleep [16], Parkinson's disease [17], and Alzheimer's disease [18]. A common feature of chimera states is their dependence on the initial conditions. Therefore, the spatial positions of the coherent and incoherent domains are not fixed. Some of the potential mechanisms that may affect the spatial distribution of chimera states in neural networks are explored in the literature. [PERSON] pointed out that modifying coupling with a tweezers method prevents the chimera collapse and also stabilizes the position [19]. [PERSON] found that it is possible to control the position of chimeras by introducing external forcing to the system [20]. [PERSON] noticed that a group of excitable oscillators can attract incoherent structures and repel coherent structures [21]. [PERSON] found that choosing one oscillator and making it link unidirectionally to the other oscillators is the minimal action to control chimeras [22]. Besides the effects on the spatial position of coherent and incoherent domains, coupling structure also affects the excitation and suppression of chimera states [23]. Despite the research mentioned above, the mechanism of how changes in coupling can effectively control the spatial distribution of coherent and incoherent regions is still not clear.