Bifurcations and Canards in the FitzHugh–Nagumo System: A Tutorial of Fast–Slow Dynamics

International Journal of Bifurcation and Chaos

2025 | journal-article

Transitions of bifurcation diagrams of a forced heteroclinic cycle

Journal of Mathematical Analysis and Applications

2025 | journal-article

High frequency forcing of an attracting heteroclinic cycle

Portugaliae Mathematica

2024 | journal-article

Stability of cycles and survival in a jungle game with four species

Dynamical Systems An International Journal

2024 | journal-article

Global planar dynamics with a star node and contracting nonlinearity

RESEARCH IN THE MATHEMATICAL SCIENCES

2024 | journal-article

Periodic Forcing of a Heteroclinic Network

Journal of Dynamics and Differential Equations

2023 | journal-article

Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock

SIAM Journal of Applied Dynamical Systems

2022 | journal-article

Asymptotic stability of robust heteroclinic networks

Nonlinearity

2020 | journal-article

Bifurcations from an attracting heteroclinic cycle under periodic forcing

Journal of Differential Equations

2020 | journal-article

Chaos in periodically forced reversible vector fields

Journal of Singularities

2020 | journal-article

Recognition of symmetries in reversible maps

Journal of Mathematical Analysis and Applications

2020 | journal-article

Stability of a heteroclinic network and its cycles: a case study from Boussinesq convection

DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL

2019 | journal-article

Global Saddles for Planar Maps

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS

2018 | journal-article

Projections of patterns and mode interactions

DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL

2018 | journal-article

On Takens' last problem: Tangencies and time averages near heteroclinic networks

Nonlinearity

2017 | journal-article

Hopf Bifurcation with Tetrahedral and Octahedral Symmetry

SIAM Journal on Applied Dynamical Systems

2016 | journal-article

LIMIT CYCLES FOR Z(2n)-EQUIVARIANT SYSTEMS WITHOUT INFINITE EQUILIBRIA

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

2016 | journal-article

Dense heteroclinic tangencies near a Bykov cycle

Journal of Differential Equations

2015 | journal-article

Discrete Symmetric Planar Dynamics

Dynamics, Games and Science

2015 | conference-paper

Hexagonal projected symmetries

ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES

2015 | journal-article

Limit cycles for a class of quintic Z(6)-equivariant systems without infinite critical points

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN

2014 | journal-article

On the projection of functions invariant under the action of a crystallographic group

Journal of Pure and Applied Algebra

2014 | journal-article

Periodic solutions in an array of coupled FitzHugh-Nagumo cells

Journal of Mathematical Analysis and Applications

2014 | journal-article

Spiralling dynamics near heteroclinic networks

Physica D: Nonlinear Phenomena

2014 | journal-article

Global dynamics for symmetric planar maps

Discrete and Continuous Dynamical Systems- Series A

2013 | journal-article

Partial Symmetry Breaking and Heteroclinic Tangencies

PROGRESS AND CHALLENGES IN DYNAMICAL SYSTEMS

2013 | conference-paper

A local but not global attractor for a ℤn-symmetric map

Journal of Singularities

2012 | journal-article

Global generic dynamics close to symmetry

Journal of Differential Equations

2012 | journal-article

The discrete Markus-Yamabe problem for symmetric planar polynomial maps

Indagationes Mathematicae

2012 | journal-article

Chaotic double cycling

Dynamical Systems

2011 | journal-article

Density of first Poincaré returns, periodic orbits, and Kolmogorov-Sinai entropy

Communications in Nonlinear Science and Numerical Simulation

2011 | journal-article

A chaotic carousel: dynamics near heteroclinic networks

Bol. Soc. Port. Mat.

2010 | journal-article

A heteroclinic network in mode interaction with symmetry

Dynamical Systems

2010 | journal-article

Switching near a network of rotating nodes

Dynamical Systems

2010 | journal-article

The geometry of Hopf and saddle-node bifurcations for waves of Hodgkin-Huxley type

Real and complex singularities

2010 | book-chapter

Projected wallpaper patterns

Real and Complex Singularities

2007 | conference-paper

Invariants for bifurcations

HOUSTON JOURNAL OF MATHEMATICS

2006 | journal-article

Simple vector fields with complex behavior

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

2006 | journal-article

Symmetries of projected wallpaper patterns

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY

2006 | journal-article

Two coupled neurons

2006 IEEE International Conference on Computational Cybernetics, ICCC

2006 | conference-paper

Dynamics near a heteroclinic network

Nonlinearity

2005 | journal-article

Flores ou ervas daninhas?

Bol. Soc. Port. Mat.

2005 | journal-article

Switching along a network

EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS

2005 | conference-paper

Loss of synchronization in partially coupled Hodgkin-Huxley equations

Bulletin of Mathematical Biology

2004 | journal-article

Stability of equilibria in equations of Hodgkin-Huxley type

Real and Complex Singularities - Contemporary Mathematics

2004 | other

Synchronization of coupled equations of Hodgkin-Huxley type

DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS

2003 | journal-article

Path formulation for a modal family

Port. Math. (N.S.)

2001 | journal-article

Counting persistent pitchforks

REAL AND COMPLEX SINGULARITIES

2000 | conference-paper

Spatial Hidden Symmetries in Pattern Formation

Pattern Formation in Continuous and Coupled Systems - The IMA Volumes in Mathematics and its Applications

1999 | book-chapter

An extension of the absolute reaction rate theory as applied to physiological rate processes

Ciência e Cultura

1997 | journal-article

Instant chaos is chaos in slow motion

Journal of Mathematical Analysis and Applications

1996 | journal-article

Singularities of equations of Hodgkin-Huxley type

DYNAMICS AND STABILITY OF SYSTEMS

1996 | journal-article

BIFURCATION OF THE HODGKIN AND HUXLEY EQUATIONS - A NEW TWIST

BULLETIN OF MATHEMATICAL BIOLOGY

1993 | journal-article

The Arrhenius plot of a physiological rate process is never linear

Ciência e Cultura

1991 | journal-article

DEGENERATE HOPF-BIFURCATION AND NERVE IMPULSE .2.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS

1989 | journal-article

DEGENERATE HOPF-BIFURCATION FORMULAS AND HILBERTS 16TH PROBLEM

SIAM JOURNAL ON MATHEMATICAL ANALYSIS

1989 | journal-article

Degenerate Hopf bifurcation and nerve impulse

SIAM Journal of Mathematical Analysis

1985 | journal-article

NOTE ON THE UNFOLDING OF DEGENERATE HOPF-BIFURCATION GERMS

JOURNAL OF DIFFERENTIAL EQUATIONS

1985 | journal-article