title: Approximate-master-equation approach for the Kinouchi-Copelli neural model on networks.
abstract: In this work, we use the approximate-master-equation approach to study the dynamics of the Kinouchi-Copelli neural model on various networks. By categorizing each neuron in terms of its state and also the states of its neighbors, we are able to uncover how the coupled system evolves with respective to time by directly solving a set of ordinary differential equations. In particular, we can easily calculate the statistical properties of the time evolution of the network instantaneous response, the network response curve, the dynamic range, and the critical point in the framework of the approximate-master-equation approach. The possible usage of the proposed theoretical approach to other spreading phenomena is briefly discussed.
authors.affiliation: Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China.
authors.forename: Chong-Yang
authors.initials: CY
authors.lastname: Wang
authors.affiliation: Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China.
authors.forename: Zhi-Xi
authors.initials: ZX
authors.lastname: Wu
authors.affiliation: Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P. R. China.
authors.forename: Michael Z Q
authors.initials: MZ
authors.lastname: Chen