A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory： the jumping distance and the waiting time, are ...A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory： the jumping distance and the waiting time, are replaced by two new ones： the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement （x^2（t）） - t^a is realized numerically and analysed theoretically, where the value of the power index a is in a region of 0 〈 a 〈 2. Particularly, the damping leads to a sub-diffusion when the impact velocities are drawn from a Gaussian density function and the super-diffusive effect is related to statistical extremes, which are called rare-though-dominant events.展开更多
In finite population games with weak selection and large population size, when the payoff matrix is constant, the one-third law serves as the condition of a strategy to be advantageous. We generalize the result to the...In finite population games with weak selection and large population size, when the payoff matrix is constant, the one-third law serves as the condition of a strategy to be advantageous. We generalize the result to the cases of environment-dependent payoff matrices which exhibit the feedback from the environment to the population. Finally, a more general law about cooperation-dominance is obtained.展开更多
基金supported by the Scientific Research Foundation of Sichuan University for Young Teachers,China (GrantNo. 2009SCU11120)
文摘A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory： the jumping distance and the waiting time, are replaced by two new ones： the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement （x^2（t）） - t^a is realized numerically and analysed theoretically, where the value of the power index a is in a region of 0 〈 a 〈 2. Particularly, the damping leads to a sub-diffusion when the impact velocities are drawn from a Gaussian density function and the super-diffusive effect is related to statistical extremes, which are called rare-though-dominant events.
文摘In finite population games with weak selection and large population size, when the payoff matrix is constant, the one-third law serves as the condition of a strategy to be advantageous. We generalize the result to the cases of environment-dependent payoff matrices which exhibit the feedback from the environment to the population. Finally, a more general law about cooperation-dominance is obtained.
