相关论文: Scenarios for the Creation of Hyperchaotic Attract…
The present paper points out to a novel scenario for formation of chaotic attractors in a class of models of excitable cell membranes near an Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics admits a simple and…
We study bifurcation behavior in periodic perturbations of two-dimensional symmetric systems exhibiting codimension-two bifurcations with a double eigenvalue when the frequencies of the perturbation terms are small. We transform the…
We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in a class of two-parameter families of periodically-perturbed differential equations defining a flow on a three-dimensional manifold.…
The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
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:…
We propose a new three-dimensional map that demonstrates the two- and three-frequency quasi-periodicity. For this map all basic quasi-periodic bifurcations are possible. The study was realized by using method of Lyapunov charts completed by…
Formation or destruction of hyperbolic chaotic attractor under parameter variation is considered with an example represented by Smale--Williams solenoid in stroboscopic Poincar\'{e} map of two alternately excited non-autonomous van der Pol…
Aperiodic dynamics which is nonchaotic is realized on Strange Nonchaotic attractors (SNAs). Such attractors are generic in quasiperiodically driven nonlinear systems, and like strange attractors, are geometrically fractal. The largest…
We study bifurcations of a symmetric equilibrium state in systems of differential equations invariant with respect to a $\mathbb{Z}_4$-symmetry. We prove that if the equilibrium state has a triple zero eigenvalue, then pseudohyperbolic…
We study bifurcations of periodic orbits in three parameter general unfoldings of certain types quadratic homoclinic tangencies to saddle fixed points. We apply the rescaling technique to first return (Poincar\'e) maps and show that the…
The probability distribution of finite-time Lyapunov exponents provides an important characterization of dynamical attractors. We study such distributions for strange nonchaotic attractors (SNAs) created through several different mechanisms…
We have identified the three prominent routes, namely Heagy-Hammel, fractalization and intermittency routes, and their mechanisms for the birth of strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic system…
In this paper, based on the classic Chua's circuit, a charge-controlled memristor is introduced to design a novel four-dimensional chaotic system. The complex dynamics of the novel chaotic system such as equilibrium points, stability,…
Discrete Lorenz attractors can be found in three-dimensional discrete maps. Discrete Lorenz attractors have similar topology to that of the continuous Lorenz attractor exhibited by the well studied 3D Lorenz system. However, the routes to…
We give a qualitative description of two main routes to chaos in three-dimensional maps. We discuss Shilnikov scenario of transition to spiral chaos and a scenario of transition to discrete Lorenz-like and figure-eight strange attractors.…
In this work, we relate the geometry of chaotic attractors of typical analytic unimodal maps to the behavior of the critical orbit. Our main result is an explicit formula relating the combinatorics of the critical orbit with the exponents…
A system of coupled two logistic maps, one periodic and the other chaotic, is studied. It is found that with the variation of the coupling strength, the system displays several curious features such as the appearance of quadrupling of…
We propose a new simple three-dimensional continuous autonomous model with two nonlinear terms and observe the dynamical behavior with respect to system parameters. This system changes the stability of fixed point via Hopf bifurcation and…
The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The…