Related references
Note: Only part of the references are listed.Generalized Hopf bifurcation of a non-smooth railway wheelset system
Pengcheng Miao et al.
NONLINEAR DYNAMICS (2020)
The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification
Yang Liu et al.
MECCANICA (2020)
Lyapunov Coefficients for Hopf Bifurcations in Systems with Piecewise Smooth Nonlinlearity
Miriam Steinherr Zazo et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2020)
Bifurcation of limit cycles from a switched equilibrium in planar switched systems
Oleg Makarenkov
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS (2019)
Hopf-like boundary equilibrium bifurcations involving two foci in Filippov systems
D. J. W. Simpson
JOURNAL OF DIFFERENTIAL EQUATIONS (2019)
The influence of localized randomness on regular grazing bifurcations with applications to impacting dynamics
David John Warwick Simpson et al.
JOURNAL OF VIBRATION AND CONTROL (2018)
Networks of piecewise linear neural mass models
S. Coombes et al.
EUROPEAN JOURNAL OF APPLIED MATHEMATICS (2018)
Shilnikov chaos, Filippov sliding and boundary equilibrium bifurcations
P. A. Glendinning
EUROPEAN JOURNAL OF APPLIED MATHEMATICS (2018)
Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces
M. R. Jeffrey et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2018)
The boundary focus-saddle bifurcation in planar piecewise linear systems. Application to the analysis of memristor oscillators
Enrique Ponce et al.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2018)
A compendium of Hopf-like bifurcations in piecewise-smooth dynamical systems
D. J. W. Simpson
PHYSICS LETTERS A (2018)
A general framework for boundary equilibrium bifurcations of Filippov systems
D. J. W. Simpson
CHAOS (2018)
The Moments Sliding Vector Field on the Intersection of Two Manifolds
Luca Dieci et al.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS (2017)
Relaxation oscillations in an idealized ocean circulation model
Andrew Roberts et al.
CLIMATE DYNAMICS (2017)
The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems
Juan Castillo et al.
NONLINEAR DYNAMICS (2017)
Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics
Rony Cristiano et al.
PHYSICA D-NONLINEAR PHENOMENA (2017)
A novel route to a Hopf bifurcation scenario in switched systems with dead-zone
P. Kowalczyk
PHYSICA D-NONLINEAR PHENOMENA (2017)
Bifurcation of Limit Cycles from a Fold-Fold Singularity in Planar Switched Systems
Oleg Makarenkov
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2017)
Hopf bifurcation of hybrid Van der Pol oscillators
Leonardo Herrera et al.
NONLINEAR ANALYSIS-HYBRID SYSTEMS (2017)
Canard solutions in planar piecewise linear systems with three zones
S. Fernandez-Garcia et al.
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL (2016)
Bistable gaits and wobbling induced by pedestrian-bridge interactions
Igor V. Belykh et al.
CHAOS (2016)
Classification of boundary equilibrium bifurcations in planar Filippov systems
Paul Glendinning
CHAOS (2016)
Synchrony in networks of coupled non-smooth dynamical systems: Extending the master stability function
Stephen Coombes et al.
EUROPEAN JOURNAL OF APPLIED MATHEMATICS (2016)
On the Number of Invariant Cones and Existence of Periodic Orbits in 3-dim Discontinuous Piecewise Linear Systems
Song-Mei Huan et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2016)
Slow-fast n-dimensional piecewise linear differential systems
R. Prohens et al.
JOURNAL OF DIFFERENTIAL EQUATIONS (2016)
Piecewise Smooth Dynamical Systems Theory: The Case of the Missing Boundary Equilibrium Bifurcations
S. J. Hogan et al.
JOURNAL OF NONLINEAR SCIENCE (2016)
Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles
James Walsh et al.
NONLINEARITY (2016)
The instantaneous local transition of a stable equilibrium to a chaotic attractor in piecewise-smooth systems of differential equations
D. J. W. Simpson
PHYSICS LETTERS A (2016)
Nonsmooth Bifurcations of Mean Field Systems of Two-Dimensional Integrate and Fire Neurons
Wilten Nicola et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2016)
Canards, Folded Nodes, and Mixed-Mode Oscillations in Piecewise-Linear Slow-Fast Systems
Mathieu Desroches et al.
SIAM REVIEW (2016)
Limit Cycle and Boundary Equilibrium Bifurcations in Continuous Planar Piecewise Linear Systems
Enrique Ponce et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2015)
Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry
Jaume Llibre et al.
JOURNAL OF NONLINEAR SCIENCE (2015)
Maximum number of limit cycles for certain piecewise linear dynamical systems
Jaume Llibre et al.
NONLINEAR DYNAMICS (2015)
Bifurcations in the Wilson-Cowan Equations with Nonsmooth Firing Rate
Jeremy Harris et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2015)
Classification of Hidden Dynamics in Discontinuous Dynamical Systems
Nicola Guglielmi et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2015)
Grazing-sliding bifurcations, border collision maps and the curse of dimensionality for piecewise smooth bifurcation theory
Paul Glendinning et al.
NONLINEARITY (2015)
Dynamics in Genetic Networks
Roderick Edwards et al.
AMERICAN MATHEMATICAL MONTHLY (2014)
Canard-like phenomena in piecewise-smooth Van der Pol systems
Andrew Roberts et al.
CHAOS (2014)
Periodic Orbits for Planar Piecewise Smooth Systems with a Line of Discontinuity
L. Dieci et al.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS (2014)
Concurrent homoclinic bifurcation and Hopf bifurcation for a class of planar Filippov systems
Liping Li et al.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2014)
On the number of limit cycles in general planar piecewise linear systems of node-node types
Song-Mei Huan et al.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2014)
Piecewise linear differential systems with two real saddles
Joan C. Artes et al.
MATHEMATICS AND COMPUTERS IN SIMULATION (2014)
Correction: A Model of Postural Control in Quiet Standing: Robust Compensation of Delay-Induced Instability Using Intermittent Activation of Feedback Control
Yoshiyuki Asai et al.
PLoS One (2014)
The discontinuous matching of two planar linear foci can have three nested crossing limit cycles
E. Freire et al.
PUBLICACIONS MATEMATIQUES (2014)
Dynamics at a Switching Intersection: Hierarchy, Isonomy, and Multiple Sliding
Mike R. Jeffrey
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2014)
Stability Analysis of Second-Order Sliding Mode Control Systems With Input-Delay Using Poincare Map
Xiangjun Li et al.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL (2013)
On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry
Jaume Llibre et al.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2013)
Existence of limit cycles in general planar piecewise linear systems of saddle-saddle dynamics
Song-Mei Huan et al.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2013)
Global qualitative analysis of a non-smooth Gause predator-prey model with a refuge
Sanyi Tang et al.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2013)
Limit cycles in a family of discontinuous piecewise linear differential systems with two zones in the plane
Denis de Carvalho Braga et al.
NONLINEAR DYNAMICS (2013)
Stochastic Regular Grazing Bifurcations
D. J. W. Simpson et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2013)
Dynamics of the Budyko Energy Balance Model
Esther R. Widiasih
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2013)
ON THE NUMBER OF LIMIT CYCLES IN GENERAL PLANAR PIECEWISE LINEAR SYSTEMS
Song-Mei Huan et al.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (2012)
DEGENERATE HOPF BIFURCATION IN NONSMOOTH PLANAR SYSTEMS
Feng Liang et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2012)
Dynamics of Simple Balancing Models with Time-Delayed Switching Feedback Control
D. J. W. Simpson et al.
JOURNAL OF NONLINEAR SCIENCE (2012)
Aspects of bifurcation theory for piecewise-smooth, continuous systems
D. J. W. Simpson et al.
PHYSICA D-NONLINEAR PHENOMENA (2012)
Invariant manifolds for nonsmooth systems
D. Weiss et al.
PHYSICA D-NONLINEAR PHENOMENA (2012)
Bifurcations of piecewise smooth flows: Perspectives, methodologies and open problems
A. Colombo et al.
PHYSICA D-NONLINEAR PHENOMENA (2012)
Saddle-node bifurcation of invariant cones in 3D piecewise linear systems
Victoriano Carmona et al.
PHYSICA D-NONLINEAR PHENOMENA (2012)
Dynamics and bifurcations of nonsmooth systems: A survey
Oleg Makarenkov et al.
PHYSICA D-NONLINEAR PHENOMENA (2012)
Generalized Hopf bifurcation emerged from a corner in general planar piecewise smooth systems
Songmei Huan et al.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2012)
Canard-Like Explosion of Limit Cycles in Two-Dimensional Piecewise-Linear Models of FitzHugh-Nagumo Type
Horacio G. Rotstein et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2012)
Canonical Discontinuous Planar Piecewise Linear Systems
Emilio Freire et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2012)
SLIDING BIFURCATIONS OF FILIPPOV TWO STAGE PEST CONTROL MODELS WITH ECONOMIC THRESHOLDS
Sanyi Tang et al.
SIAM JOURNAL ON APPLIED MATHEMATICS (2012)
Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems
P. Kowalczyk et al.
CHAOS (2011)
Friction-induced reverse chatter in rigid-body mechanisms with impacts
Arne Nordmark et al.
IMA JOURNAL OF APPLIED MATHEMATICS (2011)
Periodic orbits for perturbations of piecewise linear systems
Victoriano Carmona et al.
JOURNAL OF DIFFERENTIAL EQUATIONS (2011)
On Hopf bifurcations of piecewise planar Hamiltonian systems
Junmin Yang et al.
JOURNAL OF DIFFERENTIAL EQUATIONS (2011)
Generic bifurcations of low codimension of planar Filippov Systems
M. Guardia et al.
JOURNAL OF DIFFERENTIAL EQUATIONS (2011)
On the Gause predator-prey model with a refuge: A fresh look at the history
Vlastimil Krivan
JOURNAL OF THEORETICAL BIOLOGY (2011)
Mixed-mode oscillations in a stochastic, piecewise-linear system
D. J. W. Simpson et al.
PHYSICA D-NONLINEAR PHENOMENA (2011)
Two Degenerate Boundary Equilibrium Bifurcations in Planar Filippov Systems
Fabio Dercole et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2011)
Nondeterministic Chaos, and the Two-fold Singularity in Piecewise Smooth Flows
Alessandro Colombo et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2011)
The Geometry of Generic Sliding Bifurcations
M. R. Jeffrey et al.
SIAM REVIEW (2011)
On Hopf bifurcation in non-smooth planar systems
Maoan Han et al.
JOURNAL OF DIFFERENTIAL EQUATIONS (2010)
Generalized practical stability analysis of Filippov-type systems
Xumei Chen et al.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2010)
The time-delayed inverted pendulum: Implications for human balance control
John Milton et al.
CHAOS (2009)
HOPF BIFURCATION FOR NONSMOOTH LIENARD SYSTEMS
Xia Liu et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2009)
Existence and stability of periodic solution of a Lotka-Volterra predator-prey model with state dependent impulsive effects
Linfei Nie et al.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2009)
Discontinuity induced bifurcations in a model of Saccharomyces cerevisiae
D. J. W. Simpson et al.
MATHEMATICAL BIOSCIENCES (2009)
Bifurcation of a non-smooth planar limit cycle from a vertex
M. U. Akhmet et al.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2009)
Balancing with positive feedback: the case for discontinuous control
John Milton et al.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2009)
Unfolding a codimension-two, discontinuous, Andronov-Hopf bifurcation
D. J. W. Simpson et al.
CHAOS (2008)
Nonhyperbolic boundary equilibrium bifurcations in planar Filippov systems: A case study approach
Mario Di Bernardo et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2008)
The nature of the normal form map for soft impacting systems
Yue Ma et al.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS (2008)
Cantilever dynamics in atomic force microscopy
Arvind Raman et al.
NANO TODAY (2008)
Invariant cones for non-smooth dynamical systems
Tassilo Kuepper
MATHEMATICS AND COMPUTERS IN SIMULATION (2008)
Discontinuity-induced bifurcations of equilibria in piecewise-smooth and impacting dynamical systems
M. di Bernardo et al.
PHYSICA D-NONLINEAR PHENOMENA (2008)
On the existence and uniqueness of limit cycles in Lienard differential equations allowing discontinuities
Jaume Llibre et al.
NONLINEARITY (2008)
Experimental study of impact oscillator with one-sided elastic constraint
James Ing et al.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2008)
Neuronal Networks with Gap Junctions: A Study of Piecewise Linear Planar Neuron Models
S. Coombes
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2008)
Andronov-Hopf bifurcations in planar, piecewise-smooth, continuous flows
D. J. W. Simpson et al.
PHYSICS LETTERS A (2007)
Bifurcation analysis of piecewise smooth ecological models
Fabio Dercole et al.
THEORETICAL POPULATION BIOLOGY (2007)
Periodicity in piecewise-linear switching networks with delay
R. Edwards et al.
JOURNAL OF MATHEMATICAL BIOLOGY (2007)
A biparametric bifurcation in 3D continuous piecewise linear systems with two zones. Application to Chua's circuit
E. Freire et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2007)
A singular approach to discontinuous vector fields on the plane
Claudio A. Buzzi et al.
JOURNAL OF DIFFERENTIAL EQUATIONS (2006)
Bifurcations of equilibria in non-smooth continuous systems
R. I. Leine
PHYSICA D-NONLINEAR PHENOMENA (2006)
Analysis of a second-order sliding-mode algorithm in presence of input delays
Laura Levaggi et al.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL (2006)
Generalized Hopf bifurcation for planar Filippov systems continuous at the origin
Y Zou et al.
JOURNAL OF NONLINEAR SCIENCE (2006)
Limit cycle bifurcation in 3D continuous piecewise linear systems with two zones. Application to Chua's circuit
V Carmona et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2005)
Generalized Hopf bifurcation emanated from a corner for piecewise smooth planar systems
YK Zou et al.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2005)
Dynamic complexities in a Lotka-Volterra predator-prey model concerning impulsive control strategy
B Liu et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2005)
The focus-center-limit cycle bifurcation in symmetric 3D piecewise linear systems
E Freire et al.
SIAM JOURNAL ON APPLIED MATHEMATICS (2005)
Perturbations and Hopf bifurcation of the planar discontinuous dynamical system
MU Akhmet
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2005)
Which model to use for cortical spiking neurons?
EM Izhikevich
IEEE TRANSACTIONS ON NEURAL NETWORKS (2004)
Sliding bifurcations: A novel mechanism for the sudden onset of chaos in dry friction oscillators
M Di Bernardo et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2003)
One-parameter bifurcations in planar filippov systems
YA Kuznetsov et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2003)
Center-focus problem for discontinuous planar differential equations
A Gasull et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2003)
A survey of applications of second-order sliding mode control to mechanical systems
G Bartolini et al.
INTERNATIONAL JOURNAL OF CONTROL (2003)
Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator
XN Liu et al.
CHAOS SOLITONS & FRACTALS (2003)
Piecewise linear differential equations and integrate-and-fire neurons: Insights from two-dimensional membrane models
A Tonnelier et al.
PHYSICAL REVIEW E (2003)
A class of piecewise linear differential equations arising in biological models
JL Gouzé et al.
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL (2002)
Bifurcations of dynamical systems with sliding: derivation of normal-form mappings
M di Bernardo et al.
PHYSICA D-NONLINEAR PHENOMENA (2002)
Generalized Hopf bifurcation for non-smooth planar systems
T Küpper et al.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2001)
Planar systems of piecewise linear differential equations with a line of discontinuity
F Giannakopoulos et al.
NONLINEARITY (2001)
Zeno hybrid systems
J Zhang et al.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL (2001)
Degenerate Hopf bifurcations in discontinuous planar systems
B Coll et al.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2001)
Crossing the Hopf bifurcation in a live predator-prey system
GF Fussmann et al.
SCIENCE (2000)