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>The transition from a periodic spiking state to a periodic bursting state via a chaotic bursting state: a numerical study of a dynamical system in neurobiophysics
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The transition from a periodic spiking state to a periodic bursting state via a chaotic bursting state: a numerical study of a dynamical system in neurobiophysics
In the present study, a numerical simulation of a specific nonlinear dynamical system in neurobiophysics, namely, a mathematical model describing the dynamics of the membrane potential of snail RPa1 neurons was conducted. This model is described by a system of eight-coupled nonlinear ordinary differential equations. The study specifically focused on two system parameters of the snail RPa1 neuron model: the voltage-independent sodium conductance and voltageindependent potassium conductance. The effects of varying these parameters on the dynamics of the model were numerically simulated; the results revealed various types of transitions between different dynamical states. Interestingly, the voltage-independent potassium conductance induced a novel type of bifurcation, i.e., a periodic spiking state → a chaotic spiking state → a chaotic bursting state → a periodic bursting state, which has not been reported in previous studies of the snail RPa1 neuron model.
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