Related papers: Route to chaos in generalized logistic map
We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization.…
Ensemble of initial conditions for nonlinear maps can be described in terms of entropy. This ensemble entropy shows an asymptotic linear growth with rate K. The rate K matches the logarithm of the corresponding asymptotic sensitivity to…
We consider the $L_p$ norm estimates for homogeneous polynomials of $q$-gaussian variables ($-1\leq q\leq 1$). When $-1<q<1$ the $L_p$ estimates for $1\leq p \leq 2$ are essentially the same as the free case ($q=0$), whilst the $L_p$…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
We strengthen the standard bifurcation theorems for saddle-node, transcritical, pitchfork, and period-doubling bifurcations of maps. Our new formulation involves adding one or two extra terms to the standard truncated normal forms with…
The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
The logistic map is one of the simplest nonlinear dynamical systems that clearly exhibit the route to chaos. In this paper, we explored the evolution of the logistic map using an open-source microcontroller connected to an array of light…
We propose a new concept of generalized differentiation of set-valued maps that captures the first order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and…
In one complex variable, the cross ratio is a well-known quantity associated with four given points in the complex plane that remains invariant under linear fractional maps. In particular, if one knows where three points in the complex…
In regular dynamics, discrete maps are model presentations of discrete dynamical systems, and they may approximate continuous dynamical systems. Maps are used to investigate general properties of dynamical systems and to model various…
Motion of randomly-driven quantum nonlinear pendulum is considered. Utilizing one-step Poincar\'e map, we demonstrate that classical phase space corresponding to a single realization of the random perturbation involves domains of…
Generic 2D Hamiltonian systems possess partial barriers in their chaotic phase space that restrict classical transport. Quantum mechanically the transport is suppressed if Planck's constant h is large compared to the classical flux, h >>…
The gravity model (GM) analogous to Newton's law of universal gravitation has successfully described the flow between different spatial regions, such as human migration, traffic flows, international economic trades, etc. This simple but…
The Mullineux involution is an important map on $p$-regular partitions that originates from the modular representation theory of $\mathcal{S}_n$. In this paper we study the Mullineux transpose map and the generalized column regularization…
The Bopp's shifts will be generalized through symplectic formalism. A special procedure, like a "diagonalization", which drives the completely deformed symplectic matrix to the standard symplectic form was found as suggested by…
Let $f$ be a measurable, real function defined in a neighbourhood of infinity. The function $f$ is said to be of generalised regular variation if there exist functions $h \not\equiv 0$ and $g > 0$ such that $f(xt) - f(t) = h(x) g(t) +…
We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…
In this paper, we study the possible bifurcations of periodic orbits by reducing them to graphs. The aforementioned allows to study the genericity of routes to chaos, as well as to analyze their possible complexity. In particular, our…
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…