This paper studies a spatial duopoly model where customers are located at nodes and the demand functions are given for each node. For any fixed location of two firms, we analyze Bertrand-Nash equilibrium and derive a necessary and sufficient condition for the existence of equilibrium. We present an algorithm to compute all equilibria, provided profit functions have a finite number of peaks. The...

We introduce a self-organized critical model of punctuated equilibrium with many internal degrees of freedom (M) per site. We find exact solutions for M ! ` of cascade equations describing avalanche dynamics in the steady state. This proves the existence of simple power laws with critical exponents that verify general scaling relations for nonequilibrium phenomena. Punctuated equilibrium is des...

In this paper, we investigate the emergence of a predator-prey system with Ivlevtype functional response and reaction-diffusion. We study how diffusion affects the stability of predator-prey coexistence equilibrium and derive the conditions for Hopf and Turing bifurcation in the spatial domain. Based on the bifurcation analysis, we give the spatial pattern formation, the evolution process of th...

A coarse resolution coupled ocean-atmosphere simulation where surface albedo feedback is artificially suppressed by prescribing surface albedo is compared to one where snow and sea ice anomalies are allowed to affect surface albedo, as the model was originally designed. Canonical CO -doubling experiments were performed with both models to assess the impact of surface albedo feedback on equilibr...

In this paper the authors investigate critical phase transition characteristic of collective action by considering the mechanisms of both rational utility and psychological threshold based on the Granovetter (1978)’s threshold model. Numeric simulation is used to observe the collective dynamics with consideration of both spatial factor and social network friendship density. The authors observe ...