a b s t r a c tIn this paper we study the dynamic behaviors of an impulsive Holling II predator-prey model with mutual interference. Some sufficient conditions ensuring the prey to be extinct are obtained via the Floquent theory. We also derive some conditions for the permanence of the system by using the comparison method involving multiple Laypunov functions.Finally, the numerical simulation shows that the impulsive system has complex dynamics properties such as quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, period-doubling bifurcation, symmetry-breaking pitchfork bifurcation, period-halving bifurcation and crises.Crown
For a quartic polynomial system we investigate bifurcations of limit cycles and obtain conditions for the origin to be a center. Computing the singular point values we find also the conditions for the origin to be the eighth order fine focus. It is proven that the system can have eight small amplitude limit cycles in a neighborhood of the origin. To the best of our knowledge, this is the first example of a quartic system with eight limit cycles bifurcated from a fine focus. We also give the sufficient and necessary conditions for the origin to be an isochronous center.
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