The stationary distribution of competitive Lotka-Volterra population systems with jumps. (English) Zbl 1406.92543

Summary: Dynamics of Lotka-Volterra population with jumps (LVWJ) have recently been established (see [the third author et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 17, 6601–6616 (2011; Zbl 1228.93112); the third author and C. Yuan, J. Math. Anal. Appl. 391, No. 2, 363–375 (2012; Zbl 1316.92063)]). They provided some useful criteria on the existence of stationary distribution and some asymptotic properties for LVWJ. However, the uniqueness of stationary distribution for \(n\geq2\) and asymptotic pathwise estimation \(\lim_{t\rightarrow+\infty}(1/t)\int_0^t|X(s)|^pds\) \((p>0)\) are still unknown for LVWJ. One of our aims in this paper is to show the uniqueness of stationary distribution and asymptotic pathwise estimation for LVWJ. Moreover, some characterizations for stationary distribution are provided.


92D25 Population dynamics (general)
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