Evolution of predator–prey systems described by a Lotka–Volterra equation under random environment

By Yasuhiro Takeuchi, N. Du, N. Hieu, K. Sato. 2006

150 citations recorded by the source corpus.

Abstract In this paper, we consider the evolution of a system composed of two predator–prey deterministic systems described by Lotka–Volterra equations in random environment. It is proved that under the influence of telegraph noise, all positive trajectories of such a system always go out from any compact set of int R + 2 with probability one if two rest points of the two systems do not coincide. In case where they have the rest point in common, the trajectory either leaves from any compact set of int R + 2 or converges to the rest point. The escape of the trajectories from any compact set means that the system is neither permanent nor dissipative.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/f9c17ff9fed3febcb60c0d5771bc95aeb33a06e0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Genetics

1. Xuerong Mao
2. Daqing Jiang

In Modeling and Simulation

1. Xuerong Mao
2. Daqing Jiang
3. Ke Wang

In Public Health, Environmental and Occupational Health

1. Xuerong Mao
2. Ke Wang
3. Meng Liu
4. Daqing Jiang
5. George Yin
6. Chenggui Yuan

Citations in the corpus

• Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching (2011, background): “[13] investigated a 2-dimensional autonomous predator–prey Lotka–Volterra system with regime switching and revealed a very interesting and surprising result: If two equilibrium states of the subsystems are different, all positive trajectories of this system always exit from any compact set of R(2)+ ”
• Stochastic population dynamics under regime switching II (2007, background): “[26] consider a predator-prey Lotka–Volterra model with Markovian switching between two regimes of environment.”
• The SIS epidemic model with Markovian switching (2012, methodology): “Such an assumption is similar to that made in other papers [11, 24, 34, 36].”