Phase Synchronization Of Neuronal Oscillator Networks With Frequency-Dependent Coupling

In this paper, we explore phase synchronization in a population of neuronal oscillators with a frequency-dependent coupling in the presence of harmonic stimulus by the use of phase response curve. We derived the evolution equation of the order parameter by introducing the probability density function. Numerical simulations show that as the mode of a natural frequency is low, when the coupling strength is proportional to the natural frequency, the frequency-dependent coupling has not significant effect on phase response synchronization, and as the mode of the natural frequency is high, complete phase synchronization occurs in the population of neuronal oscillators in weak external stimulation, with increasing stimulus intensity, ultimately achieve synchronous periodic oscillation. Numerical simulations also show that when the oscillators are coupled with the weights depending on their corresponding native frequencies, the degree of synchronization reduces as the weighting exponent β increases while the mode of the natural frequency is appropriate, and the weighting exponent β can be divided into four categories while the mode of the natural frequency tends to zero, besides the phase synchronization of neuronal oscillator networks has a certain regularity in each category.