Numerical Continuation of Branch Points of Equilibria and Periodic orbits
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Summary
This work considers the three-parameter numerical continuation of branch points in dynamical systems, with emphasis on the continuation of Branch points of periodic orbits, and discusses new algorithms based on bordered matrices for both detection and continuation.
- Type
- article
- Published
- 2005-03-01
- Cited by
- 43
- References
- 17
- OpenAlex
- https://openalex.org/W2116098329
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:35750394
Keywords
Continuation, Numerical continuation, Limit (mathematics), Analytic continuation, Periodic orbits
References
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- Bifurcation Problems and their Numerical Solution
- The numerical treatment of non-trivial bifurcation points
- Collocation Software for Boundary-Value ODEs
- A General View of Minimally Extended Systems for Simple Bifurcation Points
- Continuation of periodic orbits in conservative and Hamiltonian systems
- Characterization and Computation of Generalized Turning Points
- MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
- Cellular Neural Networks and Visual Computing
- Computation of Periodic Solution Bifurcations in ODEs Using Bordered Systems
- NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS
- Numerical Continuation Methods
- Singularities and Groups in Bifurcation Theory
- Chapter 4 – Numerical Continuation, and Computation of Normal Forms
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- A timestepper approach for the systematic bifurcation and stability analysis of polymer extrusion dynamics
- Patterns of Sources and Sinks in the Complex Ginzburg-Landau Equation with Zero Linear Dispersion
- Mechanisms of wetting transitions on patterned surfaces: continuum and mesoscopic analysis
- Absolute Stability of Wavetrains Can Explain Spatiotemporal Dynamics in Reaction-Diffusion Systems of Lambda-Omega Type
- Detection of coarse-grained unstable states of microscopic/stochastic systems: a timestepper-based iterative protocol
- Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations
- Pattern Solutions of the Klausmeier Model for Banded Vegetation in Semiarid Environments V: The Transition from Patterns to Desert
- Pattern solutions of the Klausmeier Model for banded vegetation in semi-arid environments I
- On the efficiency of the equation-free closure of statistical moments: dynamical properties of a stochastic epidemic model on Erdős–Rényi networks
- Modelling the influence of activation-induced apoptosis of CD4+ and CD8+ T-cells on the immune system response of a HIV-infected patient.
- TC-HAT: A Novel Toolbox for the Continuation of Periodic Trajectories in Hybrid Dynamical Systems
- VEGETATION PATTERNS AND DESERTIFICATION WAVES IN SEMI-ARID ENVIRONMENTS: MATHEMATICAL MODELS BASED ON LOCAL FACILITATION IN PLANTS
- Elemental Periodic orbits Associated with the libration Points in the Circular Restricted 3-Body Problem
- Numerical bifurcation analysis of the bipedal spring-mass model
- New features of the software MatCont for bifurcation analysis of dynamical systems
- Seasonal forcing and multi-year cycles in interacting populations: lessons from a predator–prey model
- Numerical continuation methods for studying periodic travelling wave (wavetrain) solutions of partial differential equations
- Towards the rational design of synthetic cells with prescribed population dynamics
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