Efficient methods in the search for periodic oscillations in dynamical systems

DOI10.1016/j.jappmathmech.2010.03.004zbMath1272.70108OpenAlexW1989663520MaRDI QIDQ370459

Gennady Alekseevich Leonov

Publication date: 19 September 2013

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: http://www.sciencedirect.com/science/article/pii/S0021892810000365

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) General perturbation schemes for nonlinear problems in mechanics (70K60) Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05)

Related Items

A form of the solution to the Mathieu equation ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Hidden modalities of spirals of chaotic attractor via saturated function series and numerical results ⋮ Hidden attractor in smooth Chua systems ⋮ The behavior of hidden bifurcation in 2D scroll via saturated function series controlled by a coefficient harmonic linearization method ⋮ СКРЫТЫЕ АТТРАКТОРЫ НЕКОТОРЫХ МУЛЬТИСТАБИЛЬНЫХ СИСТЕМ С БЕСКОНЕЧНЫМ ЧИСЛОМ СОСТОЯНИЙ РАВНОВЕСИЯ ⋮ Visualization of four limit cycles of two-dimensional quadratic systems in the parameter space ⋮ Localization of hidden attractors of the generalized Chua system based on the method of harmonic balance ⋮ Hidden oscillations in dynamical systems. 16 Hilbert's problem, Aizerman's and Kalman's conjectures, hidden attractors in Chua's circuits ⋮ Analytical-Numerical Methods for Hidden Attractors’ Localization: The 16th Hilbert Problem, Aizerman and Kalman Conjectures, and Chua Circuits ⋮ Analytical-Numerical Localization of Hidden Attractor in Electrical Chua’s Circuit ⋮ Method for constructing periodic solutions of a controlled dynamic system with a cylindrical phase space ⋮ Unnamed Item

Cites Work

• Limit cycles of the Liénard equation with discontinuous coefficients
• A new class of quadratic systems
• Computation of focus values with applications
• Essays on the absolute stability theory
• A method of constructing cycles without contact around a weak focus
• Two-dimensional quadratic systems as a Liénard equation
• Cycles of two-dimensional systems: computer calculations, proofs, and experiments
• The investigation of periodic regimes of nonlinear systems on the basis of the filter hypothesis
• On the problem of estimation of the number of cycles in two-dimensional quadratic systems from the viewpoint of nonlinear mechanics
• HILBERT'S 16TH PROBLEM FOR QUADRATIC SYSTEMS: NEW METHODS BASED ON A TRANSFORMATION TO THE LIENARD EQUATION
• On features of introducing a small parameter in the investigation of nonlinear oscillations in automatic systems
• Describing functions revisited
• Frequency-Domain Methods for Nonlinear Analysis: Theory and Applications
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM
• Justification of the Describing Function Method
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item