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Interesting Features of Three-Dimensional Discrete Lotka-Volterra Dynamics
Department of Mathematics and Computer Science, Kingsborough Community College, Brooklyn, NY, USA
Department of Mathematics, Kutztown University, Kutztown, PA, USA
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, USA
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ, USA
- 1 Department of Mathematics and Computer Science, Kingsborough Community College, Brooklyn, NY, USA
- 2 Department of Mathematics, Kutztown University, Kutztown, PA, USA
- 3 Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, USA
- 4 Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ, USA
Applied Mathematics·Volume 12 (2021)·Pages 694–722·Published 12 August 2021·DOI10.4236/am.2021.128049
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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.
KeywordsDiscrete Lotka-Volterra SystemsFlip BifurcationsHigher Dimensional Neimark-Sacker Type BifurcationsChaotic Strange Attracting SetsHorseshoe Type Dynamics
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