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