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Smale, S. (1980) The Mathematics of Time: Essays on Dynamical Systems, Economic Processes, and Related Topics. Springer, New York.
https://doi.org/10.1007/978-1-4613-8101-3

has been cited by the following article:

• TITLE: Interesting Features of Three-Dimensional Discrete Lotka-Volterra Dynamics

  AUTHORS: Yogesh Joshi, Micelle Savescu, Musa Syed, Denis Blackmore

  KEYWORDS: Discrete Lotka-Volterra Systems, Flip Bifurcations, Higher Dimensional Neimark-Sacker Type Bifurcations, Chaotic Strange Attracting Sets, Horseshoe Type Dynamics

  JOURNAL NAME: Applied Mathematics, Vol.12 No.8, August 26, 2021

  ABSTRACT: Discrete Lotka-Volterra systems in one dimension (the logistic equation) and two dimensions have been studied extensively, revealing a wealth of complex dynamical regimes. We show that three-dimensional discrete Lotka-Volterra dynamical systems exhibit all of the dynamics of the lower dimensional systems and a great deal more. In fact and in particular, there are dynamical features including analogs of flip bifurcations, Neimark-Sacker bifurcations and chaotic strange attracting sets that are essentially three-dimensional. Among these are new generalizations of Neimark-Sacker bifurcations and novel chaotic strange attractors with distinctive candy cane type shapes. Several of these dynamical are investigated in detail using both analytical and simulation techniques.