Local exponential stability of several almost periodic positive solutions for a classical controlled GA-predation ecosystem possessed distributed delays

Highlights：

• We first study a class of functions having only two zeros in (−∞,+∞). By applying this result, we estimate the existence region of each solution.

• Applying the fixed point theorem of coincidence degree in nonlinear analysis, we strictly prove the existence of multiple almost-periodic positive solution from a mathematical point of view.

• Using Lyapunov theory, we derive that each almost-periodic positive solution is locally exponentially stable in its own region of existence.

• A numerical simulation verifies the correctness of main outcomes. Our research shows that the solution of this ecosystem is not unique, but there will be multiple solutions. Fortu- nately, these solutions are still locally exponentially stable, without bifurcation or chaos and other unstable situations.