Dynamic Complexity in a Prey-Predator Model with State-Dependent Impulsive Control Strategy
(a) The existence and stability of the order-1 periodic solution (the solid yellow curve represents stability of the order-1 periodic solution, the dashed red curve represents instability of the order-1 periodic solution, and the solid blue curve represents the stable order-2 periodic solution; the line denotes , where is the moment when the trajectory first met line , the line denotes , and the line denotes the critical value of parameter where the order-1 periodic solution obtain its stability again). (b) The proof of stability of the order-1 periodic solution (the solid squares represent initial points, the lines with circles denote the successor points, and the solid green circle denotes the phase point of order-1 periodic solution).
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