Related papers: Route to chaos in generalized logistic map

We study a type of object, called a pathway (generalizing pathways in the sense of P. E. Cohen [Proc. Amer. Math. Soc. 74, No. 2 (1979), 318--321]), which is useful for several set-theoretic constructions and whose existence, in a sense,…

We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…

We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…

The conductance of a ballistic quantum dot (having chaotic classical dynamics and being coupled by ballistic point contacts to two electron reservoirs) is computed on the single assumption that its scattering matrix is a member of Dyson's…

Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…

We identify a border between regular and chaotic quantum dynamics. The border is characterized by a power law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed…

We study the dynamics of a family of replicator maps, depending on two parameters. Such studies are motivated by the analysis of the dynamics of evolutionary games under selections. From the dynamics viewpoint, we prove the existence of…

This study explores the application of random matrices to track chaotic dynamics within the Chirikov standard map. Our findings highlight the potential of matrices exhibiting Wishart-like characteristics, combined with statistical insights…

The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time…

In this paper we give an example of a random perturbation of the Cat Map that produces a "global statistical attractor" in the form of a line segment. The transition probabilities for this random perturbation are smooth in some but not all…

In diverse physical systems stable oscillatory solutions devolve into more complicated dynamical behaviour through border-collision bifurcations. Mathematically these occur when a stable fixed point of a piecewise-smooth map collides with a…

We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise…

By different methods we show that for dynamical chaos in the standard map with critical golden curve the Poincar\'e recurrences P(\tau) and correlations C(\tau) asymptotically decay in time as P ~ C/\tau ~ 1/\tau^3. It is also explained why…

In the study of transport in inhomogeneous systems it is common to construct transport equations invoking the inhomogeneous Fick law. The validity of this approach requires that at least two ingredients be present in the system. First,…

Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…

A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…

Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…

The distribution of finite time observable averages and transport in low dimensional Hamiltonian systems is studied. Finite time observable average distributions are computed, from which an exponent $\alpha$ characteristic of how the…

In this work we report a new route to chaos from a resonance torus in a piecewise smooth non-invertible map of the plane into itself. The closed invariant curve defining the resonance torus is formed by the union of unstable manifolds of…

Logistic equations play a pivotal role in the study of any non linear evolution process exhibiting growth and saturation. The interest for the phenomenology, they rule, goes well beyond physical processes and cover many aspects of ecology,…