5,169 research outputs found
Constructing Attractors of Nonlinear Dynamical Systems
In a previous work, we have shown how to generate attractor sets of affine hybrid systems using a method of state space decomposition. We show here how to adapt the method to polynomial dynamics systems by approximating them as switched affine systems. We show the practical
interest of the method on standard examples of the literature
Exponential attractors for random dynamical systems and applications
The paper is devoted to constructing a random exponential attractor for some
classes of stochastic PDE's. We first prove the existence of an exponential
attractor for abstract random dynamical systems and study its dependence on a
parameter and then apply these results to a nonlinear reaction-diffusion system
with a random perturbation. We show, in particular, that the attractors can be
constructed in such a way that the symmetric distance between the attractors
for stochastic and deterministic problems goes to zero with the amplitude of
the random perturbation.Comment: 37 page
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
Design of time delayed chaotic circuit with threshold controller
A novel time delayed chaotic oscillator exhibiting mono- and double scroll
complex chaotic attractors is designed. This circuit consists of only a few
operational amplifiers and diodes and employs a threshold controller for
flexibility. It efficiently implements a piecewise linear function. The control
of piecewise linear function facilitates controlling the shape of the
attractors. This is demonstrated by constructing the phase portraits of the
attractors through numerical simulations and hardware experiments. Based on
these studies, we find that this circuit can produce multi-scroll chaotic
attractors by just introducing more number of threshold values.Comment: 21 pages, 12 figures; Submitted to IJB
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
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