Related papers: On asymptotic properties of some complex Lorenz-li…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
A method of expansion of solutions of singularly perturbed nonlinear systems in power series of small parameters is applied to the popular Lorenz model in synergetics.Simple asymptotic expressions for the solution to the model in…
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…
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…
It is well known that the Lorenz system has $Z_2$-symmetry. Using introducted in math.DS/0105147 topological covering-coloring a new representation for the Lorenz system is obtained. Deleting coloring leads to the factorized Lorenz system…
A three-component dynamic system with influence of pumping and nonlinear dissipation describing a quantum cavity electrodynamic device is studied. Different dynamical regimes are investigated in terms of divergent trajectories approaches…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
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…
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…
We discuss the unstable character of the solutions of the Lorentz-Dirac equation and stress the need of methods like order reduction to derive a physically acceptable equation of motion. The discussion is illustrated with the paradigmatic…
We are concerned with the study of the system of coupled equations of motion for a system of two-level atoms interacting with a single-mode field in the laser cavity on resonance. The passage from the equation of motion to the Lorenz…
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,…
Starting from the classical Saltzman 2D convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system…
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…
Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral…
We return to the subject of stability of infinite time asymptotics of kinetic equations. We found a model which is simpler than those studied previously and which shows unstable behavior corresponding to our arguments to appear elsewhere,…
We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be…
To improve the presentation we modified the title and used the framework of perturbation modeling of long-term dynamics so as to present the Lorentz-Abraham-Dirac equation as the lowest order, asymptotic differential relation for the…
We study the asymptotic properties of monic orthogonal polynomials (OPs) with respect to some Freud weights when the degree of the polynomial tends to infinity, including the asymptotics of the recurrence coefficients, the nontrivial…
These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…