Related papers: Patterns in the sine map bifurcation diagram
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
We numerically study bifurcations of attractors of the H\'enon map with additive bounded noise with spherical reach. The bifurcations are analysed using a finite-dimensional boundary map. We distinguish between two types of bifurcations:…
A method for the semiclassical quantization of chaotic maps is proposed, which is based on harmonic inversion. The power of the technique is demonstrated for the baker's map as a prototype example of a chaotic map.
We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both…
We study the mechanisms of pattern formation for vegetation dynamics in water-limited regions. Our analysis is based on a set of two partial differential equations (PDEs) of reaction-diffusion type for the biomass and water and one ordinary…
We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
In this paper, we consider a class of continuous maps characterized by a singularity of order $x^{q/p}$ (with $p,q \in \mathbb{N}$, $p>q$, and $(p,q)=1$) on one side of the discontinuity boundary $\Sigma$ and a linear behaviour on the other…
We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
We explore different families of quasi-periodically Forced Logistic Maps for the existence of universality and self-similarity properties. In the bifurcation diagram of the Logistic Map it is well known that there exist parameter values…
The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the…
We study a one-parameter family of quadratic maps, which serves as a template for interior point methods. It is known that such methods can exhibit chaotic behavior, but this has been verified only for particular linear optimization…
We study the dynamics of inertial particles in two dimensional incompressible flows. The particle dynamics is modelled by four dimensional dissipative bailout embedding maps of the base flow which is represented by 2-d area preserving maps.…
We apply renormalized entropy as a complexity measure to the logistic and sine-circle maps. In the case of logistic map, renormalized entropy decreases (increases) until the accumulation point (after the accumulation point up to the most…
Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The…
We numerically study, at the edge of chaos, the behaviour of the sibgle-site map $x_{t+1}=x_t-x_t/(x_t^2+\gamma^2)$, where $\gamma$ is the map parameter.
We consider dynamics of a scalar piecewise linear "saw map" with infinitely many linear segments. In particular, such maps are generated as a Poincar\'e map of simple two-dimensional discrete time piecewise linear systems involving a…
Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results…