The original Hilbert's 16th problem can be split into four parts consisting of Problems A–D. In
this paper, the progress of study on Hilbert's 16th problem is presented, and the relationship …

In 1979, Moffatt pointed out that the conventional treatment of the simplest self-exciting
homopolar disc dynamo has inconsistencies because of the neglect of induced azimuthal …

To further understand the dynamic behaviors of chaotic systems with hidden attractor and a
line equilibrium, we analyzed the fundamental dynamics of the system, including the …

This paper gives some new insights into a chaotic system. The considered system has only
one Lyapunov stable equilibrium and positive Lyapunov exponent in some certain …

In this paper, by using the Poincaré compactification in we make a global analysis of the
Lorenz system, including the complete description of its dynamic behavior on the sphere at …

In this paper, we study the global dynamics of a class of 3-dimensional Lotka--Volterra
systems with eight parameters. This system describes two predators competing for the same …

The Rikitake system is a three dimensional vector field obtained experimentally from a two-
disk dynamo apparatus, which models the geomagnetic field and is used to explain the …

To understand the complex dynamics of Kingni–Jafari system with hidden attractors, the first
objective of this paper is to study the global dynamics, and give a complete description of the …

In this paper by using the Poincaré compactification in we make a global analysis of the
Rabinovich system with and. We give the complete description of its dynamics on the sphere …

In this paper by using the Poincaré compactification of ℝ3 we describe the global dynamics
of the Lorenz system having some invariant algebraic surfaces. Of course (x, y, z)∈ ℝ3 are …