DYNAMICS OF DETERMINISTIC AND STOCHASTIC EVOLUTIONARY GAMES WITH MULTIPLE DELAYS

作者：Sirghi Nicoleta; Neamtu Mihaela^*

来源：International Journal of Bifurcation and Chaos, 2013, 23(7): 1350122.

DOI：10.1142/S0218127413501228

• Delay differential equations
• evolutionary games
• Hopf bifurcation
• mean square stability
• normal form
• stochastic dynamical system

In the present paper, we study the effect of time delays in evolutionary games with one population of users and two strategies. The case where the delays, corresponding to different strategies, are not the same is considered. The local stability of the stationary state for the replicator dynamics is analyzed. We show that there is Hopf bifurcation. The stability of the bifurcating periodic solutions is determined by using the center manifold theorem and normal form theory. The stochastic evolutionary game with delay is taken into consideration. We also study the behavior of the first and second solution moments for linear stochastic differential delay equation in the presence of white and colored noise. The last part of the paper includes numerical simulations and conclusions.

• 出版日期2013-7