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Interesting Features of Three-Dimensional Discrete Lotka-Volterra Dynamics

Applied Mathematics 2021年第8期12卷 694-722页

作者： Yogesh Joshi micelle savescu Musa Syed Denis Blackmore 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

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.

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

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SOLITONS AND CONSERVATION LAWS IN NEUROSCIENCES

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International Journal of Biomathematics 2013年第3期6卷 101-107页

作者： AN JAN BISWAS ABDUL H. KARA MICHELLE savescu ASHFAQUE H. BOKHARI F. D. ZAMAN Department of Mathematical Sciences Delaware State University Dover DE 19901-2277 USA Department of Mathematics Faculty of ScienceKing Abdulaziz University Jeddah Saudi Arabia School of Mathematics Centre for Differential EquationsContinuum Mechanics and Applications University of the Witwatersrand Johannesburg Wits 2050 South Africa Department of Mathematics Kuztown University of Pennsylvania 15200 Kutztown Road Kuztown PA 19530 USA ~Department of Mathematics and StatisticsKing Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia

This paper obtains the 1-soliton solution by the ansatz method for the proposed model that governs the propagation of solitons through the neurons. This model is an improved one that describes the solitons in neurosciences more accurately. The ansatz method is applied to obtain the 1-soliton solution to the model. The Lie symmetry analysis is subsequently applied to obtain the conservation laws for the model.

关键词： Solitons integrability conservation laws neuroscience.

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