×

Complex dynamics in a simple two-dimensional discrete system. (English) Zbl 1319.39003

Li, Changpin (ed.) et al., Recent advances in applied nonlinear dynamics with numerical analysis. Fractional dynamics, network dynamics, classical dynamics and fractal dynamics with their numerical simulations. Festschrift dedicated to Zhong-hua Yang on the occasion of his 70th birthday. Hackensack, NJ: World Scientific (ISBN 978-981-4436-45-8/hbk; 978-981-4436-47-2/ebook). Interdisciplinary Mathematical Sciences 15, 325-337 (2013).
Summary: We investigate the complex dynamics of one simple two-dimensional noninvertible discrete system. The pitchfork bifurcation, flip bifurcation and Hopf bifurcation are investigated by means of the center manifold theorem and bifurcation theory. Chaotic behavior in the sense of Li-Yorke’s definition of chaos is proved as well. Numerical simulations including bifurcation diagram, computation of the maximum Lyapunov exponent and phase portraits are provided. The numerical results verify the theoretical analysis and display the interesting complex dynamics of the proposed dynamical system.
For the entire collection see [Zbl 1261.65005].

MSC:

39A12 Discrete version of topics in analysis
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G10 Bifurcations of singular points in dynamical systems
37M20 Computational methods for bifurcation problems in dynamical systems
65P30 Numerical bifurcation problems
20H15 Other geometric groups, including crystallographic groups
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
PDFBibTeX XMLCite