Abstract
The problem of estimating reachable sets for nonlinear control systems of Lotka-Volterra type which describe the dynamics of the interaction of predators and their preys under uncertainty conditions is studied. It is assumed that we know only the restrictive set for unknown quantities and there is no additional information (for example, probabilistic, statistical, etc.) on unknown values. Applying the latest results from set-valued analysis we find the external ellipsoidal estimates of corresponding reachable sets in two cases: for systems with classical measurable control and for measure-driven (impulsive control) systems. The models under consideration can describe the behaviour of competing firms, population growth, environmental change, development of individual industries, etc. The results of modeling and numerical simulations based on proposed methods are included to illustrate the main ideas and algorithms.
12th CHAOS Conference Proceedings, 18–22 June 2019, Chania, Crete, Greece.
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Acknowledgements
The research was supported by the Russian Foundation for Basic Researches (RFBR) under Projects No. 18-01-00544-a and No. 16-29-04191-ofi-m.
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Filippova, T.F., Matviychuk, O.G. (2020). Approaches to Estimating the Dynamics of Interacting Populations with Impulse Effects and Uncertainty. In: Skiadas, C., Dimotikalis, Y. (eds) 12th Chaotic Modeling and Simulation International Conference. CHAOS 2019. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-39515-5_8
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