It is known that some predator-prey system can possess a unique limit cycle which is globally asymptotically stable. For a prototypical predator-prey system, we show that the solution curve of the limit cycle exhibits temporal patterns of a relaxation oscillator, or a Heaviside function, when certain parameter is small. MSC 2000: 34C26, 34C15, 34C07, 92D25

In this paper, the semi–ratio–dependent predator-prey system with nonmonotonic functional response on time scales is investigated. By using the coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Keywords—Semi–ratio–dependent, predator–prey system, coincidence degree, time scales.

We formulate and study a three-species population model consisting of an endemic prey (bird), an alien prey (rabbit) and an alien predator (cat). Our model overcomes several model construction problems in existing models. Moreover, our model generates richer, more reasonable and realistic dynamics. We explore the possible control strategies to save or restore the bird by controlling or eliminat...

here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.

In this paper, a reaction–diffusion system of a predator–prey model with Beddington–DeAngelis functional response is considered. This model describes a prey-taxis mechanism that is an immediate movement of the predator u in response to a change of the prey v (which leads to the collection of u). We use some approaches to prove the global existence-boundedness of classical solutions and overcome...

We examine whether children's performance on a false-belief task is impaired by task content that activates an early-developing, prepotent motivational system: predator-avoidance. In two studies (N = 46 and N = 37), children aged 3-4 years completed variants of a false-belief task that involved predator-avoidance, playmate-avoidance, prey-seeking, and playmate-seeking, respectively. The proport...

Ratio-dependent predator—prey models are favored by many animal ecologists recently as more suitable ones for predator—prey interactions where predation involves searching process. However, such models are not well studied in the sense that most results are local stability related. In this paper, we consider the global behaviors of solutions of a ratio-dependent predator—prey systems. Specifica...

Ratio-dependent predator-prey models are increasingly favored by field ecologists as an alternative or more suitable ones for predator-prey interactions where predation involves searching process. However, such models are not well studied mathematically in the past. In our recently work, we have shown that such models exhibit much richer dynamics than the traditional ones. This is especially tr...

By constructing suitable Lyapunov function and developing some new analysis techniques, a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls is studied and a sufficient condition which guarantees the globally attractive of positive solution for the predator-prey model is obtained. Moreover, the numerical simulation to the system is given to illus...

We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing predation risk can have major quantitative and qualitative effects on predator-prey cycles, including: (1) large increases in cycle period, (2) changes in ph...