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Simplest normal forms of generalized Neimark-Sacker bifurcation
Transactions of Tianjin University, 2009The 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
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Neimark‐Sacker bifurcation of a fourth order difference equation
Mathematical Methods in the Applied Sciences, 2018In 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.
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Neimark-Sacker bifurcation and chaos control in Hassell-Varley model
Journal of Difference Equations and Applications, 2017AbstractWe investigate the complex behaviour of a modified Nicholson–Bailey model. The modification is proposed by Hassel and Varley taking into account that interaction between parasitoids is taken in such a way that the searching area per parasitoid is inversely proportional to the m-th power of the population density of parasitoids.
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