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A predator-prey model with state dependent impulsive effects

Changming Ding (2014)

Annales Polonici Mathematici

We investigate a Lotka-Volterra predator-prey model with state dependent impulsive effects, in which the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered. We present some sufficient conditions to guarantee the existence and asymptotical stability of semi-trivial periodic solutions and positive periodic solutions.

Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses

Matychyn, Ivan, Chikrii, Arkadii, Onyshchenko, Viktoriia (2012)

Mathematica Balkanica New Series

MSC 2010: 34A08, 34A37, 49N70Here we investigate a problem of approaching terminal (target) set by a system of impulse differential equations of fractional order in the sense of Caputo. The system is under control of two players pursuing opposite goals. The first player tries to bring the trajectory of the system to the terminal set in the shortest time, whereas the second player tries to maximally put off the instant when the trajectory hits the set, or even avoid this meeting at all. We derive...

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