Asymptotic stability of a modified Lotka-Volterra model with small immigrations

被引：0
作者：
Takeru Tahara
Maica Krizna Areja Gavina
Takenori Kawano
Jerrold M. Tubay
Jomar F. Rabajante
Hiromu Ito
Satoru Morita
Genki Ichinose
Takuya Okabe
Tatsuya Togashi
Kei-ichi Tainaka
Akira Shimizu
Takashi Nagatani
Jin Yoshimura
机构：
[1] Shizuoka University,Department of Mathematical and Systems Engineering
[2] 3-5-1 Johoku,Graduate School of Science and Technology
[3] Naka-ku,Mathematics Division
[4] Shizuoka University,Graduate School of Integrated Science and Technology
[5] 3-5-1 Johoku,Department of General Systems Studies
[6] Naka-ku,Marine Biosystems Research Center
[7] Institute of Mathematical Sciences and Physics,Department of Biological Sciences
[8] University of the Philippines Los Baños,Department of Mechanical Engineering
[9] College,Department of Environmental and Forest Biology
[10] Shizuoka University,undefined
[11] 3-5-1 Johoku,undefined
[12] Naka-ku,undefined
[13] University of Tokyo,undefined
[14] 3-8-1 Komaba,undefined
[15] Meguro,undefined
[16] Chiba University,undefined
[17] Uchiura,undefined
[18] Kamogawa,undefined
[19] Graduate School of Science and Engineering,undefined
[20] Tokyo Metropolitan University,undefined
[21] Hachioji,undefined
[22] Shizuoka University,undefined
[23] 3-5-1 Johoku,undefined
[24] Naka-ku,undefined
[25] State University of New York College of Environmental Science and Forestry,undefined
来源：
Scientific Reports | / 8卷
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摘要：
Predator-prey systems have been studied intensively for over a hundred years. These studies have demonstrated that the dynamics of Lotka-Volterra (LV) systems are not stable, that is, exhibiting either cyclic oscillation or divergent extinction of one species. Stochastic versions of the deterministic cyclic oscillations also exhibit divergent extinction. Thus, we have no solution for asymptotic stability in predator-prey systems, unlike most natural predator-prey interactions that sometimes exhibit stable and persistent coexistence. Here, we demonstrate that adding a small immigration into the prey or predator population can stabilize the LV system. Although LV systems have been studied intensively, there is no study on the non-linear modifications that we have tested. We also checked the effect of the inclusion of non-linear interaction term to the stability of the LV system. Our results show that small immigrations invoke stable convergence in the LV system with three types of functional responses. This means that natural predator-prey populations can be stabilized by a small number of sporadic immigrants.
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