17,827 research outputs found
Hidden attractors in fundamental problems and engineering models
Recently a concept of self-excited and hidden attractors was suggested: an
attractor is called a self-excited attractor if its basin of attraction
overlaps with neighborhood of an equilibrium, otherwise it is called a hidden
attractor. For example, hidden attractors are attractors in systems with no
equilibria or with only one stable equilibrium (a special case of
multistability and coexistence of attractors). While coexisting self-excited
attractors can be found using the standard computational procedure, there is no
standard way of predicting the existence or coexistence of hidden attractors in
a system. In this plenary survey lecture the concept of self-excited and hidden
attractors is discussed, and various corresponding examples of self-excited and
hidden attractors are considered
Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
In this tutorial, we discuss self-excited and hidden attractors for systems
of differential equations. We considered the example of a Lorenz-like system
derived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, to
demonstrate the analysis of self-excited and hidden attractors and their
characteristics. We applied the fishing principle to demonstrate the existence
of a homoclinic orbit, proved the dissipativity and completeness of the system,
and found absorbing and positively invariant sets. We have shown that this
system has a self-excited attractor and a hidden attractor for certain
parameters. The upper estimates of the Lyapunov dimension of self-excited and
hidden attractors were obtained analytically.Comment: submitted to EP
Bifurcation in kinetic equation for interacting Fermi systems
The finite duration of collisions appear as time-nonlocality in the kinetic
equation. Analyzing the corresponding quantum kinetic equation for dense
interacting Fermi systems a delay differential equation is obtained which
combines time derivatives with finite time stepping known from the logistic
mapping. The responsible delay time is explicitly calculated and discussed. As
a novel feature oscillations in the time evolution of the distribution function
itself appear and bifurcations up to chaotic behavior can occur. The
temperature and density conditions are presented where such oscillations and
bifurcations arise indicating an onset of phase transition
Generation of Multi-Scroll Attractors Without Equilibria Via Piecewise Linear Systems
In this paper we present a new class of dynamical system without equilibria
which possesses a multi scroll attractor. It is a piecewise-linear (PWL) system
which is simple, stable, displays chaotic behavior and serves as a model for
analogous non-linear systems. We test for chaos using the 0-1 Test for Chaos of
Ref.12.Comment: Corresponding Author: Eric Campos-Cant\'o
Henry Kandrup's Ideas About Relaxation of Stellar Systems
Henry Kandrup wrote prolifically on the problem of relaxation of stellar
systems. His picture of relaxation was significantly more refined than the
standard description in terms of phase mixing and violent relaxation. In this
article, I summarize Henry's work in this and related areas.Comment: 11 pages. To appear in "Nonlinear Dynamics in Astronomy and Physics,
A Workshop Dedicated to the Memory of Professor Henry E. Kandrup", ed. J. R.
Buchler, S. T. Gottesman and M. E. Maho
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