Abstract
A three-species cooperative system with time delays and Lévy jumps is proposed in this paper. Firstly, by comparison method and inequality techniques, we discuss the stability in mean and extinction of species, and the stochastic permanence of this system. Secondly, by applying asymptotic method, we investigate the stability in distribution of solutions. Thirdly, utilizing ergodic method, we obtain the optimal harvesting policy of this system. Finally, some numerical examples are given to illustrate our main results.
Highlights
The Lotka–Volterra model, proposed by Lotka [1] and Volterra [2], is used to describe the evolutionary process in population dynamics, physics, and economics
Motivated by the above discussions, in this paper, we propose and consider the following three-species stochastic cooperative system with time delays and Lévy jumps:
Theorem 3.1 gives some sufficient conditions on the stability in mean and extinction of each population
Summary
The Lotka–Volterra model, proposed by Lotka [1] and Volterra [2], is used to describe the evolutionary process in population dynamics, physics, and economics. Motivated by the above discussions, in this paper, we propose and consider the following three-species stochastic cooperative system with time delays and Lévy jumps:. Let P(C([–τ , 0]; R3+)) be the space of all probability measure on C([–τ , 0]; R3+) It follows from Lemma 2.3 and Chebyshev’s inequality that the family {p(t, φ, dy)} is tight, that is, for any arbitrarily given ε > 0, there exists a compact subset K ⊆ R3+ such that P(t, φ, K) ≥ 1–ε.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
