Fractional order generalized Richards growth model with delay arguments on coupled networks

Abstract

This study aims to examine the dynamical behavior of Caputo fractional order generalized Richards growth model with delay. In order to transition from continuous time model to a discrete version, piecewise constant arguments are added to the model and thus system of difference equation are obtained from the solutions of the model in the sub- intervals. We obtain an algebraic condition where the positive equilibrium point of the discrete model with respect to changing parameter r is locally asymptotically stable. Moreover, it has been theoretically proven that the Neimark-Sacker bifurcation occurs at the positive equilibrium point of the discrete system and the direction of this bifurcation has been determined. In addition, discretized generalized Richards growth model is also considered on the globally coupled network with N=10 nodes. Numerical simulations have revealed that thecoupling strength parameter c plays a key role in the dynamical behavior of the node with the highest degree in such a complex network. Numerical simulations are performed to demonstrate the stability, bifurcations and dynamic transition of the coupled network.

Keywords

• fractional order model
• complex network
• discrete system
• stability
• neimark-sacker bifurcation