相关论文: On the non-equivalence of Lorenz System and Chen S…

Currently it is being actively discussed the question of the equivalence of various Lorenz-like systems and the possibility of universal consideration of their behavior, in view of the possibility of reduction of such systems to the same…

This article briefly introduces the generalized Lorenz systems family, which includes the classical Lorenz system and the relatively new Chen system as special cases, with infinitely many related but not topologically equivalent chaotic…

This paper reports the finding of a simple one-parameter family of three-dimensional quadratic autonomous chaotic systems. By tuning the only parameter, this system can continuously generate a variety of cascading Lorenz-like attractors,…

This note points out that the assertions of [1] are groundless and incorrect.

In the chaotic Lorenz system, Chen system and R\"ossler system, their equilibria are unstable and the number of the equilibria are no more than three. This paper shows how to construct some simple chaotic systems that can have any…

This paper describes how to determine the parameter values of the chaotic Lorenz system from one of its variables waveform. The geometrical properties of the system are used firstly to reduce the parameter search space. Then, a…

The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…

A new technique for obtaining rigorous results concerning the global dynamics of nonlinear systems is described. The technique combines abstract existence results based on the Conley index theory with computer- assisted computations. As an…

Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…

The classical Lorenz lowest order system of three nonlinear ordinary differential equations, capable of producing chaotic solutions, has been generalized by various authors in two main directions: (i) for number of equations larger than…

The dynamics of unidirectionally coupled chaotic Lorenz systems is investigated. It is revealed that chaos is present in the response system regardless of generalized synchronization. The presence of sensitivity is theoretically proved, and…

In this work, we show that a zero--Hopf bifurcation take place in the Hyperchaotic Chen system as parameters vary. Using averaging theory, we prove the existence of two periodic orbits bifurcating from the zero--Hopf equilibria located at…

The Chua system, the Lorenz system, the Chen system and The L\"u system are chaotic systems that their state space equations is very similar to Haken system which is a nonlinear model of a optical slow-fast system. These Haken-Like Sys-tems…

This paper presents the result of the investigation of chaotic oscillator synchronization. A new approach for detecting of synchronized behaviour of chaotic oscillators has been proposed. This approach is based on the analysis of different…

In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion…

In this work we demonstrate for an experimental system, that exhibits the Lorenz butterfly attractor behavior, that perfect chaotic phase synchronization cannot be achieved in systems with an unbounded distribution of intrinsic time scales.…

This paper provides a unified method for analyzing chaos synchronization of the generalized Lorenz systems. The considered synchronization scheme consists of identical master and slave generalized Lorenz systems coupled by linear state…

It is shown that Newtonian mechanics is not appropriate to compute approximate individual trajectories with small velocities in chaotic scattering. However, some global properties of the dynamical system, such as the dimension of the…

Chaos is associated with stochasticity, complex, irregular motion, etc. It has some peculiar properties such as ergodicity, highly initial value sensitivity, non-periodicity and long-term unpredictability. These pseudo random features lead…

Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…