A discrete prey-predator model preserving the dynamics of a structurally unstable Lotka-Volterra model
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概要
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Leslie's method to construct a discrete two dimensional dynamical system dynamically consistent with the Lotka-Volterra type of competing two species ordinary differential equations is applied in a newly extended manner for the Lotka-Volterra prey-predator system which is structurally unstable. We show that, independently of the time step size, the derived discrete prey-predator system is dynamically consistent with the continuous counterpart, keeping the nature of neutrally stable periodic orbit. Further, we show that the extended method to construct the discrete prey-predator system can provide a dynamically consistent model also for the logistic Lotka-Volterra one.
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