Related papers: Chaotic dynamics in three dimensions: a topologica…
In the present work we reconsider the evolutionary game theoretic models by Antoci et al. (2016, 2018) describing the dynamic outcomes arising from the interactions between patients and physicians, whose behavior is subject to clinical and…
In this paper, we investigate two heterogeneous triopoly games where the demand function of the market is isoelastic. The local stability and the bifurcation of these games are systematically analyzed using the symbolic approach proposed by…
We prove the existence of chaotic trajectories for the two body problem on a sphere. The trajectories we construct encounter near-collisions and are similar to the second species solutions of Poincar\'e of the classical 3 body problem. The…
This paper explores a novel extension of dynamic matching theory by analyzing a three-way matching problem involving agents from three distinct populations, each with two possible types. Unlike traditional static or two-way dynamic models,…
In this paper we apply the techniques of symbolic dynamics to the analysis of a labor market which shows large volatility in employment flows. In a recent paper, Bhattacharya and Bunzel \cite{BB} have found that the discrete time version of…
We study dynamics of a ball moving in gravitational field and colliding with a moving table. The motion of the limiter is assumed as periodic with piecewise constant velocity - it is assumed that the table moves up with a constant velocity…
The recently discovered Parrondo's paradox claims that two losing games can result, under random or periodic alternation of their dynamics, in a winning game: "losing+losing=winning". In this paper we follow Parrondo's philosophy of…
In the 60's Shapley provided an example of a two player fictitious game with periodic behaviour. In this game, player $A$ aims to copy $B$'s behaviour and player $B$ aims to play one ahead of player $A$. In this paper we generalize…
In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the…
Chaotic properties of symmetrical two-dimensional stadium-like billiards with elliptical arcs are studied numerically and analytically. For the two-parameter truncated elliptical billiard the existence and linear stability of several…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
"Three is a crowd" is an old proverb that applies as much to social interactions, as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…
We analyse the strategy equilibrium of dilemma games considering a payoff matrix affected by small and random perturbations on the off-diagonal. Notably, a recent work [1] reported that, while cooperation is sustained by perturbations…
The dynamics in three-dimensional billiards leads, using a Poincar\'e section, to a four-dimensional map which is challenging to visualize. By means of the recently introduced 3D phase-space slices an intuitive representation of the…
This paper introduces a class of polynomial maps in Euclidean spaces, investigates the conditions under which there exist Smale horseshoes and uniformly hyperbolic invariant sets, studies the chaotic dynamical behavior and strange…
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
We present an elementary derivation of the period-three cycles for the real quadratic map $x\mapsto x^2+c$, a fundamental model in one-dimensional discrete dynamics. Using symmetric polynomials, we obtain a complete algebraic…
A systematic framework for analyzing dynamical attributes of games has not been well-studied except for the special class of potential or near-potential games. In particular, the existing results have shortcomings in determining the…