Pattern Dynamics In Hindmarsh-Rose Neuronal Network

Distinct rhythm and self-organization in collective electric activities of neurons could be observed in a neuronal system composed of a large number of neurons.Target wave and spiral wave can regulate the collective behaviors of electrical activities in neuronal systems as a powerful “pacemaker”.Disordered states occur when normal signal propagation among neurons is disturbed and neuronal disease could be induced.In the paper,based on Hindmarsh-Rose neuron model,the method of controlled the stabilization in neuronal networks is consisted of three parts: an adaptive control method,the parameter of system regulated,changed the boundary condition,and the experimentation of condition.1.Target waves are induced by using three different ways,and then some artificial defects,which are associated with anatomical defects,are set in the network to detect the effect of defects blocking on the travelling waves.It confirms that the robustness of target waves to defects blocking depends on the intrinsic properties(ways to generate target wave)of target waves.2.Defects in the nervous system can emit continuous waves or pulses,and pacemaker-like source is generated to perturb the normal signal propagation in nervous system.the formation mechanism of defects is investigated by detecting the wave propagation induced by external forcing.It is found that defects could be induced under external periodical forcing under the boundary,and then the wave emitted from the defects can keep balance with the waves excited from external forcing.3.The initial values for nodes on the boundary of the network are selected with random values while the other nodes are selected with the same value for quiescent state.The developed spatial distribution of membrane potentials of neurons in the network will be detected by observing the spatial patterns and statistical function for sampled time series of membrane potentials.Spiral wave can be found in the network under appropriate coupling intensity and these results could be associated with self-organization in the media.4.Periodic forcing is imposed on some neurons of a two-dimensional square lattice with nearest-neighbor connection,which the local kinetics of node is described by neuron,while noise is imposed on another side of the two-dimensional lattice.The network shows spatial regularity when spiral wave is developed and it is interesting to find spiral wave can coexist with plane wave in the network.Stochastic resonance-like behavior could be observed in the two-dimensional lattice composed of neurons even if noise and periodic forcing are imposed on different areas of the network.5.On the network a few nodes of the output signal dynamic real-time detection.Using the nonlinear analysis method to diagnose the phase transition behavior caused by the slightfluctuation of the network.The collapse and instability of spiral wave,ordered states could be predicated by monitoring and analyzing the time series of some nodes.It could be useful to detect the emergence of disaster in some biological or ecological systems.