Stability and Hopf bifurcation of fractional genetic regulatory networks with diffusion 1 1 This work was partially supported by the National Natural Science Foundation of China under Grants 61473128, 61672245, 61472374, 61503129 and 61572208.

摘要

In this paper, a fractional genetic regulatory network with diffusion is proposed and several dynamic behaviors are investigated. The local stability and instability without and with diffusion are studied, respectively. The criteria for the instability with diffusion are obtained on the biological parameter and spatial parameter. Numerical simulations are given to illustrate the theoretical results and also show the effect of the fractional order on the stability and oscillations. Spatially inhomogeneous steady states which do not arise in corresponding integral-order diffusive model are found.