On the maximum number of limit cycles for a piecewise smooth differential system

DOI10.1016/j.bulsci.2020.102887zbMath1459.34086OpenAlexW3038850285MaRDI QIDQ2208967

Hongwei Shi, Yuzhen Bai, Mao'an Han

Publication date: 28 October 2020

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2020.102887

zbMATH Keywords

limit cycleaveraging theorypiecewise smooth differential system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discontinuous ordinary differential equations (34A36) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items

Limit cycles of piecewise differential equations on the cylinder ⋮ Bifurcation of limit cycles of a piecewise smooth Hamiltonian system

Cites Work

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• Averaging methods for finding periodic orbits via Brouwer degree.
• A new result on averaging theory for a class of discontinuous planar differential systems with applications
• Limit cycles of a second-order differential equation
• Upper estimates for the number of periodic solutions to multi-dimensional systems
• On the birth of limit cycles for non-smooth dynamical systems
• Averaging theory at any order for computing periodic orbits
• Averaging theory for discontinuous piecewise differential systems
• Periodic solutions of nonlinear periodic differential systems with a small parameter
• Averaging methods of arbitrary order, periodic solutions and integrability
• Nonsmooth Bifurcations of Mean Field Systems of Two-Dimensional Integrate and Fire Neurons
• Neuronal Networks with Gap Junctions: A Study of Piecewise Linear Planar Neuron Models
• ON THE MAXIMUM NUMBER OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC EQUATIONS BY AVERAGE METHOD
• Bifurcations in the Wilson--Cowan Equations with Nonsmooth Firing Rate
• BIFURCATION ANALYSIS OF AN IMPACT MODEL FOR FOREST FIRE PREDICTION
• Higher order averaging theory for finding periodic solutions via Brouwer degree
• On the Gause predator-prey model with a refuge: a fresh look at the history

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