Periodic solutions for an equation governing dynamics of a renewable resource subjected to Allee effects. (English) Zbl 1197.34078

Padhi, Seshadev; Srinivasu, P. D. N.; Kumar, G. Kiran

Nonlinear Anal., Real World Appl. 11, No. 4, 2610-2618 (2010).

Summary: The minimum number of positive periodic solutions admitted by a non-autonomous scalar differential equation is estimated. This result is employed to find the minimum number of positive periodic solutions admitted by a model describing the dynamics of a renewable resource that is subjected to Allee effects in a seasonally varying environment. The Allee effect refers to a decrease in the population growth rate at low population densities. The Leggett-Williams multiple fixed point theorem is used to establish the existence of positive periodic solutions.

MSC:

34C60	Qualitative investigation and simulation of ordinary differential equation models
34C25	Periodic solutions to ordinary differential equations
92D40	Ecology
47N20	Applications of operator theory to differential and integral equations

Keywords:

renewable resource; Allee effect; periodic solutions; positive solution

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