Methods of qualitative theory in nonlinear dynamics
Explore this paper's citation graph
- Type
- book
- Published
- 1998-01-01
- Cited by
- 658
- References
- 69
- OpenAlex
- https://openalex.org/W1582770960
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:117941475
Keywords
Homoclinic orbit, Heteroclinic bifurcation, Dynamical systems theory, Saddle, Bifurcation
References
- Smooth Invariant Manifolds and Normal Forms
- Chua's Circuit: A Paradigm for Chaos
- On Moduli of Systems with a Structurally Unstable Homoclinic POINCARÉ Curve
- Chua's circuit: rigorous results and future problems
- On the reduction principle in the theory of stability of motion
- SYSTEMS WITH A HOMOCLINIC CURVE OF MULTIDIMENSIONAL SADDLE-FOCUS TYPE, AND SPIRAL CHAOS
- LORENZ EQUATION AND CHUA’S EQUATION
- Die Stabilitätsfrage bei Differentialgleichungen
- ON SYSTEMS WITH A SADDLE-FOCUS HOMOCLINIC CURVE
- The C1 Brunovsky Hypothesis
- Chua's circuit and the qualitative theory of dynamical systems
- On models with non-rough Poincare´ homoclinic curves
- An algorithm for finding all vertices of convex polyhedral sets
- ON A POINCARÉ-BIRKHOFF PROBLEM
- The stable, center-stable, center, center-unstable, unstable manifolds
- A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE
- ON THE GENERALITY OF THE UNFOLDED CHUA'S CIRCUIT
- Dynamical phenomena in systems with structurally unstable Poincare homoclinic orbits.
- Some global aspects of homoclinic bifurcations of vector fields
- EQUIVALENCE AND DECOMPOSITION OF VECTOR FIELDS ABOUT AN ELEMENTARY CRITICAL POINT.
Cited by
- Mechanisms of Multistability in Neuronal Models
- Cycles in continuous and discrete dynamical systems : computations, computer-assisted proofs, and computer experiments
- Neural cartography: Computer assisted Poincare return mappings for biological oscillations
- The anti-integrable limit
- Selected general problems in chaos theory and nonlinear dynamics
- SLOW DRIFT IN A SLOW-FAST HAMILTONIAN SYSTEM
- Homoclinic Tangencies of an Arbitrary Order in Newhouse Domains
- Extension of Generalized Modeling and Application to Problems from Cell Biology
- Calcul moulien et théorie des formes normales classiques et renormalisées
- Semidefinite Programming and Stability of Dynamical System
- A Mechanism of Co-Existence of Bursting and Silent Regimes of Activities of a Neuron
- Adaptive State Feedback Control of Lorenz Systems to Its Non-Trivial Equilibrium
- Nonlinear dynamics of pattern recognition and optimization
- On Periodic Motion and Bifurcations in Three-Dimensional Nonlinear Systems
- Mechanisms of the Coregulation of Multiple Ionic Currents for the Control of Neuronal Activity
- Blue sky catastrophe as applied to modeling of cardiac rhythms
- Bifurcations and Multistability of the Oscillations of a Three-Dimensional System
- Computational Study in Chaotic Dynamical Systems and Mechanisms for Pattern Generation in Three-Cell Networks
- On Homoclinic Orbits to Center Manifolds in Hamiltonian Systems
- Strange attractors with various equilibrium types
Related papers
- Limit cycle bifurcations near homoclinic and heteroclinic loops via stability-changing of a homoclinic loop☆
- Homoclinic snaking near a heteroclinic cycle in reversible systems
- Codimension 2 reversible heteroclinic bifurcations with inclination flips
- Homoclinic and heteroclinic bifurcations in piecewise smooth systems via stability-changing method
- Analytics of homoclinic bifurcations in Three-Dimensional Systems
- Homoclinic and Heteroclinic Orbits for a Liénard System
- Bifurcations near homoclinic orbits with symmetry
- Homoclinic Interactions Near a Triple-Zero Degeneracy in Chua's equation