Dynamical Analysis Of Two Classes Of Morris-lecar-like Models

With the continuous development and improvement of computational neuroscience, the firing patterns and the bifurcation theory of various neuron models have been widely studied, for example, the Hodgkin-Huxley model and the Morris-Lecar model and so on, this lay the foundation for us to study deeply of the nervous system’s information coding. We mainly studies firing pattern and dynamics properties of two classes of modified three-dimensional Morris- Lecar – Like model in this paper. The Morris-Lecar-Like model mentioned in this paper is mainly by adding different external current stimulation based on the original model to make the modified model produces abundant dynamic behavior. Main results are as follows:In the third chapter,we mainly study the firing patterns and dynamic behavior of MLLⅠmodel. Firstly,we study the effects of calcium equilibrium potential,membrane capacitance and time scale factor on neuronal firing activities by numerical simulation and we get rich firing patterns such as spike firing,bursting firing and irregular firing and so on. Secondly,we found the transformation between different kinds of firing patterns caused by these physiological parameters appear typical nonlinear dynamic phenomenon including period-doubling bifurcation,and periodic adding bifurcation phenomena. On this basis,we study dynamics properties of these bursting firing patterns by employing fast-slow dynamics theory and calculating the first Lyapunov coefficient of the Hopf bifurcation point H.In the fourth chapter,we mainly study the firing patterns and dynamics properties of MLLⅡ model. We find a kind of complex firing patterns named as mixed-mode oscillations(MMOs) by adjusting potassium equilibrium potential,membrane capacitance and external current stimulation. Mixed-mode oscillations(MMOs) in neuronal systems are oscillatory patterns of activity consisting of subthreshold(or membrane potential) oscillations interspersed with action potentials(or spikes). Neuronal systems will present more complex MMOs and more chaotic regions when given more complicated alternating current stimulus. We deeply study the special phenomenon combined amplitude ratio with ISIs sequence.