Research On Spontaneous Generation Of Ordered Waves By HR Neural Network

Experimental results show that planar waves and spiral waves can occur spontaneously in cerebral cortex under certain conditions in cerebral cortex.Spiral waves occur frequently in the mammalian neocortex in vivo,both during pharmacologically induced oscillations and during sleep-like states.The epileptic seizure may also exhibit spiral wave behavior.Spiral wave is a form of propagating wave rotating around a spiral wave tip,so it can organize and modulate cortical population activity on the mesoscopic scale and may contribute to both normal cortical processing and to pathological patterns of activity such as those found in epilepsy,so as to affect the function of the brain.Therefore,it is of great significance for understanding brain function and treating epileptic disease to understand the generation mechanism and dynamic behavior of spiral wave in neural network.It was found that the noise can induce spiral waves.What factors except noise are involved in the spontaneous formation of spiral wave and planar wave in cerebral cortex has not be studied yet.In this paper,we use two-dimensional array of Hindmarsh-Rose(HR)neuron to study whether spiral wave can occur spontaneously in the two-dimensional array of HR neurons that evolves from the initial state with a random phase distribution.The system has the nearest-neighbor excitatory coupling.We studied two problems.One is the effect of the neuronal state on the spontaneous formation of spiral wave.The other is the effect of long-rang inhibitory coupling between neurons on the spontaneous formation of spiral wave in the network.The research results about the first question are as follows: Whether spiral wave can occur spontaneously in the system depends on the state of the single HR neuron,initial state of system and coupling strength.Especially,the state of the single HR neuron plays a central role.When the single HR neuron is in the state of period 1 spike,multiple spiral waves and spiral pairs can be generated spontaneously in the system for a certain range of coupling strength.In this case,the formations of spiral waves are completely independent of the initial state of the system,and as long as choosing an appropriate coupling strength,a single spiral wave can be found in the system.Furthermore,when the coupling strength exceeds a certain threshold value,the system will exhibit three kinds of dynamical behaviors,and correspond to three kinds of the different initial states,respectively.When system evolves from the first kind of initial state,the single spiral wave can be found occasionally in the system.When the system evolves from the second or third kind of initial state,the oscillation with intermittently global synchronization and oscillation death can be observed in the system,respectively.When a single HR neuron is in the state of period 2 spike,the spiral wave can appear spontaneously in the system only when the phase distribution of the initial state approaches to a uniform distribution.Moreover,the range of coupling strength on the generation of spiral wave is smaller than that of period 1 spike.When the single HR neuron is in a higher periodic state,it is difficult to generate spontaneously spiral wave in the system.The research results about the second question are as follows: When the inhibitory coupling strength is small,the spontaneous formation of ordered wave does not generally appear in the network.The larger inhibitory coupling strength,the easier the system generates an ordered wave for sufficiently large strength of excitatory coupling.The appearance of differently ordered waves is closely related to the initial state of system and coupling strength.When the excitatory and inhibitory coupling strengths are properly selected,the system can spontaneously appear maze pattern,planar wave,single spiral wave,multiple spiral waves,pairs of spiral waves rotating in the opposite direction,two-arm spiral wave,target wave and inward square wave.The occurrence probabilities of spiral wave and maze pattern reach 27.5% and 21.5%,respectively.Maze pattern is composed of many plane waves with different propagation directions.The occurrence probabilities of other ordered waves are small.The above results can help us understand the self-organization phenomenon in the cerebral cortex.The results are also of guiding significance for the treatment of epilepsy.