Neimark-sacker bifurcation - Open Access .click

Journal of Difference Equations and Applications, 2014
In this paper we show how a change of a box dimension of orbits of two-dimensional discrete dynamical systems is connected to their bifurcations in a nonhyperbolic fixed point. This connection is already shown in the case of one-dimensional discrete dynamical systems and Hopf bifurcation for continuous systems.
Lana Horvat Dmitrovic
exaly +4 more sources

Neimark‐Sacker bifurcation of a fourth order difference equation

Mathematical Methods in the Applied Sciences, 2018
In this article, we study stability and bifurcation of a fourth order rational difference equation. We give condition for local stability, and we show that the equation undergoes a Neimark‐Sacker bifurcation. Moreover, we consider the direction of the Neimark‐Sacker bifurcation. Finally, we numerically validate our analytical results.
Marwan Aloqeili
exaly +3 more sources

Simplest normal forms of generalized Neimark-Sacker bifurcation

Transactions of Tianjin University, 2009
The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system. It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation are expressed in polar coordinates, then all odd order terms must, in general, remain in the normal forms. In this paper, five theorems are
Qichang Zhang, Zhang Qichang
exaly +2 more sources

mathematics
stability
neimark–sacker bifurcation

flip bifurcation
bifurcation theory for difference equations
bifurcation

qa1-939
delay
population dynamics general