15,327 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
Dynamics of delay induced composite multi-scroll attractor and its application in encryption
This work was supported in part by NSFC (60804040, 61172070), Key Program of Nature Science Foundation of Shaanxi Province (2016ZDJC-01), Innovative Research Team of Shaanxi Province(2013KCT-04), Fok Ying Tong Education Foundation Young Teacher Foundation(111065), Chao Bai was supported by Excellent Ph.D. research fund (310-252071603) at XAUT.Peer reviewedPostprin
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
Reduction of dimension for nonlinear dynamical systems
We consider reduction of dimension for nonlinear dynamical systems. We
demonstrate that in some cases, one can reduce a nonlinear system of equations
into a single equation for one of the state variables, and this can be useful
for computing the solution when using a variety of analytical approaches. In
the case where this reduction is possible, we employ differential elimination
to obtain the reduced system. While analytical, the approach is algorithmic,
and is implemented in symbolic software such as {\sc MAPLE} or {\sc SageMath}.
In other cases, the reduction cannot be performed strictly in terms of
differential operators, and one obtains integro-differential operators, which
may still be useful. In either case, one can use the reduced equation to both
approximate solutions for the state variables and perform chaos diagnostics
more efficiently than could be done for the original higher-dimensional system,
as well as to construct Lyapunov functions which help in the large-time study
of the state variables. A number of chaotic and hyperchaotic dynamical systems
are used as examples in order to motivate the approach.Comment: 16 pages, no figure
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