Analytical-numerical methods of finding hidden oscillations in multidimensional dynamical systems

DOI10.1134/S0012266114130023zbMath1351.37268MaRDI QIDQ2345824

I. M. Burkin, Nguen Ngok Khien

Publication date: 21 May 2015

Published in: Differential Equations (Search for Journal in Brave)

zbMATH Keywords

attractorsnumerical methodshidden attractor

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Attractors of solutions to ordinary differential equations (34D45) Stability theory for smooth dynamical systems (37C75) Approximation methods and numerical treatment of dynamical systems (37M99)

Related Items (16)

Method of ``transition into space of derivatives: 40 years of evolution ⋮ Global problems for differential inclusions. Kalman and Vyshnegradskii problems and Chua circuits ⋮ An approach to generating extremely multistable chaotic systems ⋮ СКРЫТЫЕ АТТРАКТОРЫ НЕКОТОРЫХ МУЛЬТИСТАБИЛЬНЫХ СИСТЕМ С БЕСКОНЕЧНЫМ ЧИСЛОМ СОСТОЯНИЙ РАВНОВЕСИЯ ⋮ ОБ ОДНОМ ПОДХОДЕ К ПОСТРОЕНИЮ ХАОТИЧЕСКИХ СИСТЕМ-ХАМЕЛЕОНОВ ⋮ Hidden and unstable periodic orbits as a result of homoclinic bifurcations in the Suarez-Schopf delayed oscillator and the irregularity of ENSO ⋮ Hidden Attractors on One Path: Glukhovsky–Dolzhansky, Lorenz, and Rabinovich Systems ⋮ Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity ⋮ Generation of extremely multistable systems based on Lurie systems ⋮ Theory of Differential Inclusions and Its Application in Mechanics ⋮ Graphical Structure of Attraction Basins of Hidden Chaotic Attractors: The Rabinovich–Fabrikant System ⋮ Hidden attractors in dynamical systems ⋮ Unnamed Item ⋮ Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system ⋮ Scenario of the Birth of Hidden Attractors in the Chua Circuit ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits
• Aircraft control with anti-windup compensation
• Delayed feedback on the 3-D chaotic system only with two stable node-foci
• Localization of hidden Chua's attractors
• Algorithm for constructing counterexamples to the Kalman problem
• Algorithm for localizing Chua attractors based on the harmonic linearization method
• Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems
• On the stability in the large of nonlinear systems in the critical case of two zero roots
• Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors
• The buffer phenomenon in multidimensional dynamical systems
• Hidden attractor in smooth Chua systems
• Dynamical behaviors of a chaotic system with no equilibria
• Elementary quadratic chaotic flows with no equilibria
• An equation for continuous chaos
• Analytical-Numerical Methods for Hidden Attractors’ Localization: The 16th Hilbert Problem, Aizerman and Kalman Conjectures, and Chua Circuits
• HIDDEN ATTRACTORS IN DYNAMICAL SYSTEMS. FROM HIDDEN OSCILLATIONS IN HILBERT–KOLMOGOROV, AIZERMAN, AND KALMAN PROBLEMS TO HIDDEN CHAOTIC ATTRACTOR IN CHUA CIRCUITS
• HARMONIC BALANCE ANALYSIS OF THE GENERALIZED CHUA'S CIRCUIT
• Frequency-Domain Methods for Nonlinear Analysis: Theory and Applications
• Analytical-Numerical Localization of Hidden Attractor in Electrical Chua’s Circuit
• SIMPLE CHAOTIC FLOWS WITH ONE STABLE EQUILIBRIUM
• Cost Function Based on Gaussian Mixture Model for Parameter Estimation of a Chaotic Circuit with a Hidden Attractor
• Similarity Model of an Explosion in a Rarefied Atmosphere

This page was built for publication: Analytical-numerical methods of finding hidden oscillations in multidimensional dynamical systems