A class of autocatalytic reaction networks based on template-dependent ligation and higher-order catalysis is analysed. Apart from an irreversible ligation reaction we consider only reversible aggregation steps that provide a realistic description of molecular recognition. The overall dynamics can be understood by means of replicator equations with highly non-linear interaction functions. The d...

Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations. We here show that similar noise-sustained trajectories arise in game dynamical learning, where the stochasticity has a different origin: agents sample a finit...

Evolutionary game dynamics in finite populations is typically subject to noise, inducing effects which are not present in deterministic systems, including fixation and extinction. In the first part of this paper we investigate the phenomenon of drift reversal in finite populations, taking into account that drift is a local quantity in strategy space. Secondly, we study a simple imitation dynami...

In this article, we focus on studying the passivity properties of different versions replicator dynamics (RD). The RD represents a deterministic monotone nonlinear dynamic, which allows incorporation distribution population types through fitness function. We use tools for control theory, in particular, to study stability when it is action with evolutionary games. theory us identify class games ...

As of today, the most credible scientific paradigm pertaining to the origin of life on Earth is undoubtedly the RNA World scenario. It is built on the assumption that catalytically active replicators (most probably RNA-like macromolecules) may have been responsible for booting up life almost four billion years ago. The many different incarnations of nucleotide sequence (string) replicator model...

To understand the emergence and sustainment of cooperative behavior in interacting collectives, we perform global convergence analysis for replicator dynamics a large, well-mixed population individuals playing repeated snowdrift game with four typical strategies, which are always cooperate (ALLC), tit-for-tat (TFT), suspicious (STFT), defect (ALLD). The dynamical model is 3-D ordinary different...