Zhu Haoqi, Wang Mao-Xiang, Lai Pik-Yin
School of Science, Nanjing University of Science and Technology, Nanjing 210094, China.
Department of Physics and Center for Complex Systems, National Central University, Chung-Li District, Taoyuan City 320, Taiwan, Republic of China.
Phys Rev E. 2018 May;97(5-1):052413. doi: 10.1103/PhysRevE.97.052413.
The population dynamics of two interacting species modeled by the Lotka-Volterra (LV) model with general parameters that can promote or suppress the other species is studied. It is found that the properties of the two species' isoclines determine the interaction of species, leading to six regimes in the phase diagram of interspecies interaction; i.e., there are six different interspecific relationships described by the LV model. Four regimes allow for nontrivial species coexistence, among which it is found that three of them are stable, namely, weak competition, mutualism, and predator-prey scenarios can lead to win-win coexistence situations. The Lyapunov function for general nontrivial two-species coexistence is also constructed. Furthermore, in the presence of spatial diffusion of the species, the dynamics can lead to steady wavefront propagation and can alter the population map. Propagating wavefront solutions in one dimension are investigated analytically and by numerical solutions. The steady wavefront speeds are obtained analytically via nonlinear dynamics analysis and verified by numerical solutions. In addition to the inter- and intraspecific interaction parameters, the intrinsic speed parameters of each species play a decisive role in species populations and wave properties. In some regimes, both species can copropagate with the same wave speeds in a finite range of parameters. Our results are further discussed in the light of possible biological relevance and ecological implications.
研究了由具有可促进或抑制另一物种的一般参数的洛特卡 - 沃尔泰拉（LV）模型所模拟的两个相互作用物种的种群动态。发现两个物种的等斜线性质决定了物种间的相互作用，导致种间相互作用相图中出现六种状态；即，LV模型描述了六种不同的种间关系。四种状态允许非平凡的物种共存，其中发现其中三种是稳定的，即弱竞争、互利共生和捕食 - 猎物情景可导致双赢的共存情况。还构建了一般非平凡的两种物种共存的李雅普诺夫函数。此外，在物种存在空间扩散的情况下，动态过程可导致稳定的波前传播并可改变种群分布图。通过解析和数值解研究了一维中的传播波前解。通过非线性动力学分析解析地获得了稳定波前速度，并通过数值解进行了验证。除了种间和种内相互作用参数外，每个物种的固有速度参数在物种种群和波特性中起决定性作用。在某些状态下，两个物种可以在有限的参数范围内以相同的波速共同传播。根据可能的生物学相关性和生态意义进一步讨论了我们的结果。
