Heteroclinic Trajectory and Hopf Bifurcation in an Extended Lorenz System

DOI10.1142/S0218127418501110zbMath1401.34021OpenAlexW2890804219MaRDI QIDQ4691111

Publication date: 18 October 2018

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127418501110

zbMATH Keywords

Lyapunov function Hopf bifurcation project method homoclinic and heteroclinic trajectories extended Lorenz system

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Dynamics of the general Lorenz family
Heteroclinic orbits in the \(T\) and the Lü systems
Nonlinear analysis in a Lorenz-like system
A novel hyperchaotic system with infinitely many heteroclinic orbits coined
On singular orbits and a given conjecture for a 3D Lorenz-like system
The past in short hypercycles
On the stabilizing effect of predators and competitors on ecological communities
Heteroclinic connections between periodic orbits in planar restricted circular three body problem. II
Dynamics of a new Lorenz-like chaotic system
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
Local and global behavior near homoclinic orbits
Global bifurcations and chaos. Analytical methods
The heteroclinic cycle in the model of competition between \(n\) species and its stability
A case study for homoclinic chaos in an autonomous electronic circuit. A trip from Takens-Bogdanov to Hopf-Sil'nikov
Heteroclinic connections between periodic orbits in planar restricted circular three-body problem -- a computer-assisted proof
Cellular buckling in long structures
Mathematical problems for the next century
Hopf bifurcations in an extended Lorenz system
Existence of a singularly degenerate heteroclinic cycle in the Lorenz system and its dynamical consequences. I
Breaking projective chaos synchronization secure communication using filtering and generalized synchronization
The Lorenz equations: bifurcations, chaos, and strange attractors
Quantitative universality for a class of nonlinear transformations
Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity
Dynamics of a hyperchaotic Lorenz-type system
Bifurcation analysis of the Watt governor system
Dynamical properties and simulation of a new Lorenz-like chaotic system
Hopf bifurcation and heteroclinic orbit in a 3D autonomous chaotic system
On the nature of turbulence
Heteroclinic, Homoclinic and Closed Orbits in the Chen System
HOPF BIFURCATION IN A CALCIUM OSCILLATION MODEL AND ITS CONTROL: FREQUENCY DOMAIN APPROACH
Hidden Hyperchaotic Attractors in a Modified Lorenz–Stenflo System with Only One Stable Equilibrium
More Dynamical Properties Revealed from a 3D Lorenz-like System
New Heteroclinic Orbits Coined
Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model
HOMOCLINIC AND HETEROCLINIC ORBITS AND BIFURCATIONS OF A NEW LORENZ-TYPE SYSTEM
Complex Dynamics in the Unified Lorenz-Type System
ON HOMOCLINIC AND HETEROCLINIC ORBITS OF CHEN'S SYSTEM
Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system
Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems
Nonlinear Aspects of Competition Between Three Species
Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
Deterministic Nonperiodic Flow
Chaos in Dynamical Systems
Introduction to Applied Nonlinear Dynamical Systems and Chaos
Invariant algebraic surfaces of the Lorenz system
Infinitely Many Heteroclinic Orbits of a Complex Lorenz System
Elements of applied bifurcation theory

This page was built for publication: Heteroclinic Trajectory and Hopf Bifurcation in an Extended Lorenz System