Study Of Bursting Pattern Within Complex Nonlinear Systems And Their Control

The pre-B(?)tzinger complex,located in the mammalian brainstem,is the key site for mammalian to the generation of respiratory rhythms.Different firing rhythms can occur spontaneously in the pre-B(?)tzinger complex.External stimuli can cause the firing rhythm to change from one pattern to another,which will make the body to produce different physiological effects.Therefore,understanding the relationship between different firing patterns of neurons and external stimuli will help us to reveal the mechanism of diseases caused by external stimuli.In this paper,we study an improved pre-B(?)tzinger complex neuron model under the washout filter controller with the coupling of electrical synapses.By fast and slow time scales,single-and two-parameter bifurcation analysis,we investigated the bursting patterns and their transition mechanisms of the pre-B(?)tzinger complex under control.We discussed the influence of Hopf bifurcation on bursting patterns and their transition mechanisms and how the position of the Hopf bifurcation and limit cycle control the bursting pattern.According to the definition of phase function,the synchronization of bursting patterns of two coupled neurons is also discussed.In-phase,anti-phase and mixed bursting of firing patterns under electric synapse coupling are investigated.The results show that the position of Hopf bifurcation and the amplitude of the limit cycle of the system can be controlled by applying a filter controller.So the generation and transition of the bursting pattern in the system can be controlled.The position of the Hopf bifurcation has a great effect on the bursting pattern.When the amplitude of the system trajectory is different,the bursting pattern of the system will change accordingly.The coupling strength under the electrical synaptic coupling has a great influence on the bursting pattern of the system.The system presents different firing patterns when the coupling strength is in different values.