Abstract
In this paper, we discuss a discrete competitive system based on density dependence to obtain a set of sufficient conditions for the existence and asymptotic stability of the equilibrium of systems. By obtaining the optimal harvest strategy of systems through the extreme value method and the discrete Pontryagin maximum principle, we provide a theoretical direction for the actual production.
Highlights
Stability and permanence of a biological system have been studied by several authors [ – ]
4 Conclusion This paper qualitatively analyzes a competitive system in situations that are density constrained
We have discussed the stability of equilibrium point in different regions, improved methods of proof in reference
Summary
Stability and permanence of a biological system have been studied by several authors [ – ]. It is more reasonable to consider the discrete system’s capture It will keep the biological balance but it will save time and produce more economic revenue for fishermen. In this paper, we consider the following discrete two species competitive system and discuss the system’s stability and capturing strategy, xn = xn(a – b xn – c yn) – E xn = P (xn, yn),. Let E , E (E , E > ) be the capture intensity of the two populations (that is, fishing effort multiplies the capture coefficients) (E + E = E), and let the capture per unit time be proportional to the stock and population, a > E and a > E Under this assumption, we can get the following competitive capture systems.
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