A Reduced Order Modeling Framework for Strongly Perturbed Nonlinear Dynamical Systems Near Arbitrary Trajectory Sets

Neural biology (92C20) Nonlinear systems in control theory (93C10) Perturbations in control/observation systems (93C73) System structure simplification (93B11)

Cites Work

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Time optimal control of spiking neurons
Fundamental limits of forced asynchronous spiking with integrate and fire dynamics
Tools to detect structures in dynamical systems using jet transport
Chemical oscillations, waves, and turbulence
A data-driven approximation of the koopman operator: extending dynamic mode decomposition
Mathematical foundations of neuroscience
Inertial manifolds for nonlinear evolutionary equations
Integral manifolds and inertial manifolds for dissipative partial differential equations
Isochrons and phaseless sets
On contraction analysis for non-linear systems
Greater accuracy and broadened applicability of phase reduction using isostable coordinates
Weakly coupled oscillators in a slowly varying world
Phase reduction and phase-based optimal control for biological systems: a tutorial
Spectrum of the Koopman operator, spectral expansions in functional spaces, and state-space geometry
Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits
Phase-amplitude dynamics in terms of extended response functions: invariant curves and Arnold tongues
Phase-amplitude reduction of limit cycling systems
Phase-amplitude descriptions of neural oscillator models
Phase-amplitude response functions for transient-state stimuli
Fokker-Planck and Fortet equation-based parameter estimation for a leaky integrate-and-fire model with sinusoidal and stochastic forcing
Multi-timescale systems and fast-slow analysis
Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics
Extending Phase Reduction to Excitable Media: Theory and Applications
Optimal Chaotic Desynchronization for Neural Populations
Introduction to Perturbation Methods
Applied Koopmanism
Global Stability Analysis Using the Eigenfunctions of the Koopman Operator
A Computational and Geometric Approach to Phase Resetting Curves and Surfaces
Spectral analysis of nonlinear flows
Derivatives and Perturbations of Eigenvectors
A New Frame for an Old (Phase) Portrait: Finding Rivers and Other Flow Features in the Plane
A Variational Method for Analyzing Stochastic Limit Cycle Oscillators
Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems
Introduction to Applied Nonlinear Dynamical Systems and Chaos
On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
Analysis of Fluid Flows via Spectral Properties of the Koopman Operator
The infinitesimal phase response curves of oscillators in piecewise smooth dynamical systems
Data-driven inference of high-accuracy isostable-based dynamical models in response to external inputs
An Adaptive Phase-Amplitude Reduction Framework without $\mathcal{O}(\epsilon)$ Constraints on Inputs
Optimal Control of Oscillation Timing and Entrainment Using Large Magnitude Inputs: An Adaptive Phase-Amplitude-Coordinate-Based Approach
LOR for Analysis of Periodic Dynamics: A One-Stop Shop Approach
Low dimensional behavior of large systems of globally coupled oscillators
A Contraction Theory Approach to Singularly Perturbed Systems
CHIMERA STATES IN A RING OF NONLOCALLY COUPLED OSCILLATORS
Averaging methods in nonlinear dynamical systems
The geometry of biological time.