Stability of Cycles in a Game of Rock-Scissors-Paper-Lizard-Spock

We study a system of ordinary differential equations in that is used as model both population dynamics and game theory known to exhibit heteroclinic network consisting the union four types elementary cycles. show asymptotic stability for parameter values range compatible with dynamics. obtain estimates relative attractiveness each one cycles by computing their indices. For ensuring we relate properties cycle others. In particular, three if them has weak form attractiveness, then other two are completely unstable. also existence an open region space where all unstable asymptotically stable, giving rise intricate been observed numerically authors.