In this paper, an extended Rikitake system is studied. Several issues, such as Hopf
bifurcation, coexistence of stable equilibria and hidden attractor, and dynamics analysis at …

The aim of this paper is to give some new insights into the Shimizu–Morioka system x˙= y,
y˙= x− λ y− xz, z˙=− α z+ x 2, from the integrability point of view. Firstly, we propose a linear …

In this paper, a novel qualitative method is proposed to analyze the transient stability of
power systems. Unlike the traditional methods, this method can illustrate the structural …

We study the local Hopf bifurcations of codimension one and two, which occur in the
Shimizu–Morioka system. This system is a simplified model proposed for studying the …

We present a global dynamical analysis of the following quadratic differential system ̇ x= a
(yx), ̇ y\!=\! dy-xz, ̇ z\!=\!-bz+ fx^ 2+ gxy x˙= a (yx), y˙= dy-xz, z˙=-bz+ fx 2+ gxy, where (x, y …

In this paper, global dynamics of the Maxwell–Bloch system is discussed. First, the complete
description of its dynamic behavior on the sphere at infinity is presented by using the …

The investigation of dynamical behaviors for fractional-order chaotic systems is a new trend
recently. This article is numerically concerned with the Shimizu-Morioka model with a …

An invariant algebraic surface is calculated for a 3D autonomous quadratic system. Also, the
dynamics near finite singularities and near infinite singularities on the invariant algebraic …

Abstract top Hopf bifurcation, dynamics at infinity and robust modified function projective
synchronization (RMFPS) problem for Sprott E system with quadratic perturbation were …

This chapter investigates the control of continuous time Shimizu–Morioka chaotic system
with unknown system parameters by means of three different control approaches, namely …