We investigate the dynamics of three-strategy (rock–paper–scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval T . Taking T as a bifurcation parameter, we demonstrate the existence of (non-degenerate) Hopf bifurcations in these systems and present an analysis of the resulting limit cycles using Lindstedt’s me...

In this paper, we address stability and robustness properties of hybrid limit cycles for a class of hybrid systems with multiple jumps in one period. The main results entail equivalent characterizations of stability of hybrid limit cycles for hybrid systems. The hybrid limit cycles may have multiple jumps in one period and the jumps are allowed to occur on sets. Conditions guaranteeing robustne...

We give a new and short proof of the characterization of monodromic nilpotent critical points.We also calculate the first generalized Lyapunov constants in order to solve the stability problem. We apply the results to several families of planar systems obtaining necessary and sufficient conditions for having a center. Our method also allows us to generate limit cycles from the origin.

We consider a generalized pendulum equation depending on the scalar parameter μ having for μ = 0 a limit cycle Γ of the second kind and of multiplicity three. We study the bifurcation behavior of Γ for −1 ≤ μ ≤ ( √ 5 + 3)/2 by means of a Dulac-Cherkas function.

This paper explores equilibrium and optimal matching behavior in constant returns to scale search economies with heterogeneous agents. We show that optimal matching behavior may involve a nontrivial limit cycle, and that there may exist a continuum of cyclical perfect foresight equilibria. These results hold for a generic set of parameter values. They are due to a trading externality (Diamond 1...

For a given differential system, a limit cycle is a periodic orbit isolated in the set of all its periodic orbits. Within the qualitative theory of differential systems, the study of their limit cycles is one of the main topics. Many questions are considered on the limit cycles of the differential systems in R2. Thus, one of the main lines of research for such systems is the study of how many l...

If Γ 1 and Γ 2 are limit groups and S ⊂ Γ 1 × Γ 2 is of type FP 2 then S has a subgroup of finite index that is a product of at most two limit groups.

We study, with various methods, the high temperature phase transition for the N-component φ 4 theory in the large N limit. Our results fully confirm a previous investigation of the problem, for arbitrary N , with the method of the average potential. The phase transition is of the second order with an effectively three-dimensional critical behaviour.