Simulations of the dynamics of two consumers $C_1, C_2$ and two resources $R_1, R_2$ are presented within the Rosenzweig-MacArthur model (RMA). Consumers $i=1,2$ share their time/effort devoted to particular resources; for each $i$, the consumption rates of the two resources are ${\beta }_i$ and $1-{\beta }_i$. Here, the model dynamics are enriched by the evolution of these rates over time. Namely, at discrete time instants, the consumer with a smaller density $C_i$ updates her rates to imitate the behavior of the more successful opponent, while the rates of the latter remain unchanged. These rules can be written as ‘‘lose-shift’’ and ‘‘win-stay,’’ respectively, where ‘‘shift’’ is directed to imitate the temporal winner. The phase diagram in the plane (${\beta }_1,{\beta }_2$) shows periodic orbits and chaos. The latter behavior is more prominent when resources are acquired unevenly. Compared with three alternative strategies, the ‘‘win-stay, lose-shift’’ strategy is an equilibrium in both the periodic and chaotic regimes.

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• Bifurcations
• Control & applications of chaos
• Population dynamics
• Coupled oscillators