Periodicity in a logistic type system with several delays. (English) Zbl 1061.34050

Summary: With the help of a continuation theorem based on Gaines and Mawhin’s coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of the following logistic-type system with several delays \[ \frac{du(t)}{dt}=u(t)\left[a(t)-\sum^m_{j=1}b_j(t) \biggl(u\bigl(t-\tau_j(t)\bigr)\biggr)^{\theta_j} \right], \] where \(a(t)\), \(b_j(t)\) are positive periodic continuous functions with periodic \(\omega>0\), \(\tau_j(t)\) are nonnegative continuous periodic functions with periodic \(\omega>0\). After that, by constructing a suitable Lyapunov functional, some sufficient conditions which guarantee the stability of the positive periodic solutions are obtained.


34K13 Periodic solutions to functional-differential equations
34K20 Stability theory of functional-differential equations
Full Text: DOI


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