Generalized Hamiltonian dynamics and chaos in evolutionary games on networks

Evolutionary dynamics for bimatrix games: a Hamiltonian system?

We review some properties of the evolutionary dynamics for asymmetric conflicts, give a simplified approach to them, and present some new results on the stability and bifurcations occurring in these conservative systems. In particular, we compare their dynamics to those of Hamiltonian systems.

Evolutionary games on networks and payoff invariance under replicator dynamics

The commonly used accumulated payoff scheme is not invariant with respect to shifts of payoff values when applied locally in degree-inhomogeneous population structures. We propose a suitably modified payoff scheme and we show both formally and by numerical simulation, that it leaves the replicator dynamics invariant with respect to affine transformations of the game payoff matrix. We then show ...

Hamiltonian dynamics and distributed chaos in DNA

It is shown that distributed chaos, generated by Hamiltonian DNA dynamics with spontaneously broken time translational symmetry, imprints itself on the DNA sequence of Arabidopsis thaliana (a model plant for genetic sequencing and mapping) and of the NRXN1 and BRCA2 human genes (as an example). The base-stacking interactions in the DNA duplex and degenerate codon groups have been discussed in t...

Population Games And Evolutionary Dynamics

Evolutionary Games and Local Dynamics

Evolutionary games have been introduced by Maynard Smith and Price [1973] in the early 70’s with the aim to study the stability of populations in time. In the general model, a population consists of finitely many different types that interact randomly with each other, where each interaction leads to fitness payoffs for each of the types involved. Consequently, the population distribution over t...