A New Class of Two-dimensional Chaotic Maps with Closed Curve Fixed Points
Jiang, H; Liu, Y; Wei, Z; et al.Zhang, L
Date: 30 June 2019
Journal
International Journal of Bifurcation and Chaos
Publisher
World Scientific Publishing
Publisher DOI
Abstract
This paper constructs a new class of two-dimensional maps with closed curve fixed points.
Firstly, the mathematical model of these maps is formulated by introducing a nonlinear function. Different types of fixed points which form a closed curve are shown by choosing proper
parameters of the nonlinear function. The stabilities of these ...
This paper constructs a new class of two-dimensional maps with closed curve fixed points.
Firstly, the mathematical model of these maps is formulated by introducing a nonlinear function. Different types of fixed points which form a closed curve are shown by choosing proper
parameters of the nonlinear function. The stabilities of these fixed points are studied to show
that these fixed points are all non-hyperbolic. Then a computer search program is employed to
explore the chaotic attractors in these maps, and several simple maps whose fixed points form
different shapes of closed curves are presented. Complex dynamical behaviours of these maps are
investigated by using the phase-basin portrait, Lyapunov exponents, and bifurcation diagrams.
Engineering
Faculty of Environment, Science and Economy
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