Methods of continuation and their implementation in the COCO software platform with application to delay differential equations
DOI10.1007/s11071-021-06841-1zbMath1517.65129arXiv2104.12261WikidataQ115381664 ScholiaQ115381664MaRDI QIDQ6117149
Mingwu Li, Harry J. Dankowicz, Zaid Ahsan, Jan Sieber
Publication date: 16 August 2023
Published in: Nonlinear Dynamics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2104.12261
Lagrange multipliersconstrained optimizationdelay differential equationsadjoint equationsgraph representationsproblem regularizationphase response curvesimplicitly defined manifoldsmulti-segment boundary-value problems
Numerical computation of solutions to systems of equations (65H10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Numerical bifurcation problems (65P30) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04) Numerical methods for functional-differential equations (65L03)
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Cites Work
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- A unified parameter identification method for nonlinear time-delay systems
- Phase reduction of weakly perturbed limit cycle oscillations in time-delay systems
- The Mackey-Glass model of respiratory dynamics: review and new results
- Numerical methods for computing sensitivities for ODEs and DDEs
- A multi-interval Chebyshev collocation approach for the stability of periodic delay systems with discontinuities
- A parametric study on supersonic/hypersonic flutter behavior of aero-thermo-elastic geometrically imperfect curved skin panel
- Solving boundary value problems for delay differential equations by a fixed-point method
- Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs
- MANPAK: A set of algorithms for computations on implicitly defined manifolds
- On a boundary value problem for delay differential equations of population dynamics and Chebyshev approximation
- Advanced multibody system dynamics: simulation and software tools
- Weakly connected neural networks
- Continuation of periodic orbits in conservative and Hamiltonian systems
- Numerical bifurcation analysis for ODEs
- Designing efficient software for solving delay differential equations
- Numerical computation of connecting orbits in delay differential equations
- Asymptotic phase revisited
- Model reduction of non-densely defined piecewise-smooth systems in Banach spaces
- A numerical approach for the bifurcation analysis of nonsmooth delay equations
- Optimization along families of periodic and quasiperiodic orbits in dynamical systems with delay
- Numerical continuation in nonlinear experiments using local Gaussian process regression
- Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction
- Mackey-Glass equation with variable coefficients
- Numerical continuation methods for dynamical systems. Path following and boundary value problems.
- Practical bifurcation and stability analysis
- Collocation Methods for the Computation of Periodic Solutions of Delay Differential Equations
- pde2path - A Matlab Package for Continuation and Bifurcation in 2D Elliptic Systems
- Algorithm 652
- A stochastic method for global optimization
- Continuation-based Computation of Global Isochrons
- Simulating, Analyzing, and Animating Dynamical Systems
- Staged Construction of Adjoints for Constrained Optimization of Integro-Differential Boundary-Value Problems
- STABILITY CALCULATIONS FOR PIECEWISE-SMOOTH DELAY EQUATIONS
- Global bifurcations of the Lorenz manifold
- The Numerical Computation of Connecting Orbits in Dynamical Systems
- A Lin's method approach to finding and continuing heteroclinic connections involving periodic orbits
- TC-HAT ($\widehat{TC}$): A Novel Toolbox for the Continuation of Periodic Trajectories in Hybrid Dynamical Systems
- Communities in Networks
- An arc-length method including line searches and accelerations
- A unified theory of first and second order conditions for extremum problems in topological vector spaces
- Computation, Continuation and Bifurcation Analysis of Periodic Solutions of Delay Differential Equations
- Introduction to Numerical Continuation Methods
- Optimization in Bifurcation Problems using a Continuation Method
- Invariant manifolds and global bifurcations
- Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems
- MULTIPLE PARAMETER CONTINUATION: COMPUTING IMPLICITLY DEFINED k-MANIFOLDS
- Recipes for Continuation
- Nonlinear response of swirling premixed flames to helical flow disturbances
- Convergence Analysis of Collocation Methods for Computing Periodic Solutions of Retarded Functional Differential Equations
- A Continuation Approach to Computing Phase Resetting Curves
- An adaptive polynomial based forward prediction algorithm for multi-actuator real-time dynamic substructuring
- Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL
- MATCONT
- SlideCont: An Auto97 driver for bifurcation analysis of Filippov systems
- Computation of the Phase Response Curve: A Direct Numerical Approach
- Computing One-Dimensional Global Manifolds of Poincaré Maps by Continuation
- Continuation of Quasi-periodic Invariant Tori
- A trust region method based on interior point techniques for nonlinear programming.
- Implementing Radau IIA methods for stiff delay differential equations
- Invariant spectral foliations with applications to model order reduction and synthesis