9,218 research outputs found
Study of the earth's magnetic field with the aid of radiation belts
Electron belt detected during flights of Elektron-1 and Elektron-
Interrelation Between the Irregular Events in the Ionosphere of the Aurora Zone and the Disturbances in the Outer Radiation Belt
Interrelation between irregular events in lower ionosphere of auroral zone and disturbances in outer radiation bel
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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