Author(s)

Yogesh Joshi¹, Micelle Savescu², Musa Syed³, Denis Blackmore⁴

¹Department of Mathematics and Computer Science, Kingsborough Community College, Brooklyn, NY, USA.
²Department of Mathematics, Kutztown University, Kutztown, PA, USA.
³Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, USA.
⁴Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ, USA.

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.

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

Joshi, Y. , Savescu, M. , Syed, M. and Blackmore, D. (2021) Interesting Features of Three-Dimensional Discrete Lotka-Volterra Dynamics. Applied Mathematics, 12, 694-722. doi: 10.4236/am.2021.128049.