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Stability and Monotonicity of Lotka–Volterra Type Operators

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Abstract

In the present paper, we investigate stability of trajectories of Lotka–Volterra (LV) type operators defined in finite dimensional simplex. We prove that any LV type operator is a surjection of the simplex. It is introduced a new class of LV-type operators, called MLV type ones, and we show that trajectories of the introduced operators converge. Moreover, we show that such kind of operators have totally different behavior than \({\mathbf {f}}\)-monotone LV type operators.

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Acknowledgments

The authors acknowledge the MOHE Grant ERGS13-024-0057, and the authors are also grateful the Junior Associate scheme of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy.

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  1. Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box 141, 25710, Kuantan, Pahang, Malaysia

    Farrukh Mukhamedov & Mansoor Saburov

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  1. Farrukh Mukhamedov
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  2. Mansoor Saburov
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Correspondence to Farrukh Mukhamedov.

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Mukhamedov, F., Saburov, M. Stability and Monotonicity of Lotka–Volterra Type Operators. Qual. Theory Dyn. Syst. 16, 249–267 (2017). https://doi.org/10.1007/s12346-016-0190-3

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  • DOI: https://doi.org/10.1007/s12346-016-0190-3

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