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Existence and attractivity of a periodic solution for a ratio-dependent Leslie system with feedback controls. (English) Zbl 1208.34078
Summary: A ratio-dependent Leslie system with feedback controls is studied. By using comparison and continuation theorems, and based on coincidence degree and by constructing a suitable Lyapunov function, some sufficient and necessary conditions for the existence and global attractivity of periodic solutions are obtained. An example shows that the obtained criteria are easily verifiable.
MSC:
34C60Qualitative investigation and simulation of models (ODE)
34D20Stability of ODE
34C05Location of integral curves, singular points, limit cycles (ODE)
47N20Applications of operator theory to differential and integral equations
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