Formation of local heterogeneity under energy collection in neural networks

Static distribution of intracellular and extracellular ions can induce the spatial distribution of electric field in the cell, while stochastic diffusion and propagation of ions can generate channel current accompanied by the magnetic field. In fact, the field energy (including magnetic and electric fields) in each cell or neuron can be changed under external stimuli or the deformation of shape. Furthermore, energy pumping occurs, and the synaptic connection is created adaptively to keep energy balance when more neurons are clustered in the same region because of electromagnetic field superposition. For a synchronous and homogeneous network, all neurons keep energy balance with the adjacent neurons, and the network becomes uniform and identical. For cardiac tissue and biological media, local heterogeneity such as sinoatrial node can emit continuous wave front, and target waves are propagated to regulate the neural activities and heartbeat rhythm. In this paper, the Hamilton energy in a simple neuron model is calculated according to the Helmholtz theorem, and more neurons are clustered to build a regular network (chain network and square array). The creation and growth of synapse connection are controlled to pump energy, and local heterogeneity is formed by taming one intrinsic parameter when more energy is accumulated in a few neurons in the network. These results indicate that asymmetrical energy transport will induce the occurrence of heterogeneity in the network, and adaptive synaptic regulation on neurons is activated to keep local energy balance before reaching perfect synchronization. When external stimuli with diversity in intensity are applied, neurons are excited with energy diversity, and possible shape deformation is induced to keep local energy balance. As a result, heterogeneity is developed in a local area.