[PDF] Top 20 Population and evolutionary adaptive dynamics of a stochastic predator-prey model

... an evolutionary fitness function which is based on stochastic differential system and investigates the adaptive dynamics of the proposed ...a stochastic predator-prey ... See full document

... the population cannot be ignored, which has attracted the attention of biologists and has become a new research ...the stochastic Gilpin-Ayala predator-prey system with time-varying delays, ... See full document

... A predator-prey model with Beddington-DeAngelis functional response and disease in the predator population is proposed, corresponding to the deterministic system, a stochastic ... See full document

... Population systems have long been an important theme in mathematical biology due to their universal existence and importance. As a result, interest in mathematical models for populations with interaction between ... See full document

... the population density of the pest and the natural enemy at time t, respectively, r represents the intrinsic growth rate, K is the carrying capacity parameter, β denotes the attack rate of the predator, λ ... See full document

... the population sizes of the prey and the predator, respectively; r i , a ij , τ and δ i (i, j = 1, 2) are given positive ...investigated model (M); see ...of stochastic ... See full document

... a stochastic predator–prey model with Allee effect and Lévy ...of stochastic differential equations, we prove that the model has a unique global positive solution starting from the ... See full document

... deterministic population systems with toxins effect and established the theoretical persistence-extinction thresholds for their ...chain model and n- dimensional factualistic system, ... See full document

... any model of species dynamics with delays is an approx- imation at ...delay prey-predator system, see, ...delay population systems with Bedding-DeAngelis functional response, see ... See full document

... on stochastic predator-prey population dynamics in spatially extended systems, and the investigation of dynamical correlations and fluctuations beyond the realm of the standard ... See full document

... of population inte- ractions should take the effects of time delay into account [13] [14] [15] ...about stochastic predator-prey system with Beddingtons-DeAngelis and time ...the ... See full document

... of stochastic predator-prey populations in toxic ...the model established in this paper possesses non-negative solutions as this is essential in any population dynamics ...the ... See full document

... However, population system is often affected by environmental noise, and there are many scholars who have studied the dynamics of stochastic models with toxicant [4] [5] [6] ... See full document

... and evolutionary dynamics of populations mirrored by the large number of mathematical models devoted to it in the scientific literature ...of population and local (or global) stability of equilibria ... See full document

... the stochastic system is a more realistic model to describe the world than the deter- ministic ...deterministic model (1.2) will die out, in the sense that the prey population remains ... See full document

... Mathematical model for prey-predator was developed inde- pendently by Aefred James Lotka [19] and Vito Volterra ...a predator in an ecological system depends strongly on functional ...a ... See full document

... When k = 0-8 in this system, the 'normal' approximation suggests that the mean passage time to zero should be of the order of 35 steps for both species. Both of these means are somewhat [r] ... See full document

... for stochastic population models, for example, stochastic persistence in probability (see [, ]) or a new definition of stochastic permanence (see ... See full document

... In the predator-prey interaction, predation is viewed as a "disease" of the predator transmitted by the prey.. In this approach, the predator population is partitioned into hungr[r] ... See full document

... The general approach for solving Equation 2 consists of the following steps: 1 Assume that the impact of predator on prey population growth is negligible, 2 Predator population declines [r] ... See full document