Yunshyong Chow

Imitation, local interaction, and coordination

This paper analyzes players’ long-run behavior in evolutionary coordination games with imitation and one-dimensional local interaction. Players are assumed to interact with their two neighbors and to imitate actions with the highest average payoffs. We find that the payoff-dominant equilibrium survives in the long run with positive probability. The results derive the conditions under which both risk-dominant-strategy and payoff-dominant-strategy takers co-exist in the long run. The risk-dominant equilibrium is the unique long-run equilibrium for the remaining cases. This study extends and complements the analyses of Eshel et al. (Am Econ Rev 88:157–179, 1998) and Vega-Redondo (Evolution, games, and economic behaviour, 1996). Combining Alós-Ferrer and Weidenholzer’s (Econ Lett 93:163–168, 2006; J Econ Theory 14:251–274, 2008) and our results, we conclude that players’ long-run behavior varies with imitation rules and information collecting modes. Finally, we show the convergence rate to all the long-run equilibria.

On a heat conduction problem by myshkis

Let Tn=1,T2,T3..... be recurrently defined by The sequence (Tn) appeared in a heat conduction problem studied by Myshkis (J. Differ. Equations Appl. 3, 1997, 89-91). He proposed as an open problem the asymptotic expression for Tn It is shown in this paper that Tn, is increasing and limn Tn/n=π2/2

Cannibalism in discrete-time predator-prey systems.

In this study, we propose and investigate a two-stage population model with cannibalism. It is shown that cannibalism can destabilize and lower the magnitude of the interior steady state. However, it is proved that cannibalism has no effect on the persistence of the population. Based on this model, we study two systems of predator–prey interactions where the prey population is cannibalistic. A sufficient condition based on the nontrivial boundary steady state for which both populations can coexist is derived. It is found via numerical simulations that introduction of the predator population may either stabilize or destabilize the prey dynamics, depending on cannibalism coefficients and other vital parameters.

ON THE ASYMPTOTIC BEHAVIOR OF HEATING TIMES

An infinite homogeneous d-dimensional medium initially is at zero temperature, u=0. A heat impulse is applied at the origin, raising the temperature there to a value greater than a constant value u...

Multiple attractors in a Leslie–Gower competition system with Allee effects

We investigate asymptotic dynamics of the classical Leslie–Gower competition model when both competing populations are subject to Allee effects. The system may possess four interior steady states. It is proved that for certain parameter regimes both competing populations may either go extinct, coexist or one population drives the other population to extinction depending on initial conditions.

On multidimensional discrete-time Beverton–Holt competition models

Following Ackleh et al. (2005), we study the multidimensional discrete-time competitive Beverton–Holt equations with equal interspecific competition coefficients. It is shown that competitive exclusion occurs if only one species has the largest carrying capacity. Otherwise, all the species with the largest carrying capacity coexist. In the former case, the system is globally asymptotically stable. In the latter case, the system has a linear stable manifold.

Allee effects in a Ricker-type predator–prey system

We study a discrete host–parasitoid system where the host population follows the classical Ricker functional form and is also subject to Allee effects. We determine basins of attraction of the local attractors of the single population model when the host intrinsic growth rate is not large. In this situation, existence and local stability of the interior steady states for the host–parasitoid interaction are completely analysed. If the hosts intrinsic growth rate is large, then the interaction may support multiple interior steady states. Linear stability of these steady states is provided.

Coexistence in a discrete competition model with dispersal

We propose a discrete-time competition model between two populations to study the effects of dispersal upon population interactions. It is assumed that dispersal occurs after reproduction and in synchrony. We first analyse a two-patch single species population model with no interspecific competition. Based on these results, we derive sufficient conditions for population coexistence. It is proved that the system is uniformly persistent and possesses a unique coexisting equilibrium.

The Asymptotic Behavior of Simulated Annealing Processes with Absorption

For a large class (satisfying a Perron-Frobenius property) of simulated annealing processes with an absorbing state

Templeting and self-assembly

a