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Existence of positive almost periodic or ergodic solutions for some neutral nonlinear integral equations. (English) Zbl 1240.42021
The paper investigates the dynamics of a population affected by constant and proportional harvesting. The authors present four models for distributed delay logistic equations with harvesting. Under some conditions these equations are studied by the equations \[ x'(t)=r x(t) \left (1-\int _0^{t}x(\xi )\, d\xi \right ) - H(x), \]
\[ x'(t)=r x(t) \left (1-\int _0^{t}\alpha e^{-\alpha (t-\xi )} x(\xi )\, d\xi \right ) - H(x), \] where \(H(x)=h\) or \(H(x)=hx\) (\(r,h,\alpha \) are positive constants). The behavior of solutions, the stability of the equilibria and the existence of a Hopf bifurcation are studied. A numerical simulation is performed to illustrate the obtained results.

42A75 Classical almost periodic functions, mean periodic functions
45G10 Other nonlinear integral equations