# Resonant forcing of nonlinear systems of differential equations.

@article{Gintautas2008ResonantFO, title={Resonant forcing of nonlinear systems of differential equations.}, author={Vadas Gintautas and Alfred W. H{\"u}bler}, journal={Chaos}, year={2008}, volume={18 3}, pages={ 033118 } }

We study resonances of nonlinear systems of differential equations, including but not limited to the equations of motion of a particle moving in a potential. We use the calculus of variations to determine the minimal additive forcing function that induces a desired terminal response, such as an energy in the case of a physical system. We include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the… Expand

#### 13 Citations

Optimal entrainment with smooth, pulse, and square signals in weakly forced nonlinear oscillators

- Mathematics
- 2014

Abstract A physical limit of entrainability of nonlinear oscillators is considered for an external weak signal (forcing). This limit of entrainability is characterized by the optimization problem… Expand

Optimal Control and Synchronization of Dynamic Ensemble Systems

- Computer Science
- 2014

The focus of this dissertation is on novel analytical paradigms and constructive control design methods for practical ensemble control problems, and a computational method for the synthesis of minimum-norm ensemble controls for time-varying linear systems. Expand

Synchronization limit of weakly forced nonlinear oscillators

- Mathematics
- 2014

Nonlinear oscillators exhibit synchronization (injection-locking) to external periodic forcings, which underlies the mutual synchronization in networks of nonlinear oscillators. Despite its history… Expand

The conservation laws with Lie symmetry analysis for time fractional integrable coupled KdV–mKdV system

- Mathematics
- 2018

Abstract In this paper, the fractional Lie symmetry method has been implemented for getting similarity reduction and conservation laws for time fractional integrable coupled KdV–mKdV system. Firstly,… Expand

Optimal waveform for the entrainment of a weakly forced oscillator.

- Physics, Medicine
- Physical review letters
- 2010

A theory for obtaining a waveform for the effective entrainment of a weakly forced oscillator is presented and the theory is tested in chemical entrainments experiments in which oscillations close to and farther away from a Hopf bifurcation exhibited sinusoidal and higher harmonic nontrivial optimal waveforms, respectively. Expand

Entrainment Limit of Weakly Forced Nonlinear Oscillators

- Physics
- 2015

Nonlinear oscillators exhibit entrainment (injection locking) to external periodic forcings. Despite its history of entrainment, and the wide utility of injection locking to date, it has been an open… Expand

Global dynamics of Chua Corsage Memristor circuit family: fixed-point loci, Hopf bifurcation, and coexisting dynamic attractors

- Physics
- 2020

This paper presents an in-depth and rigorous mathematical analysis of a family of nonlinear dynamical circuits whose only nonlinear component is a Chua Corsage Memristor (CCM) characterized by an… Expand

Stochastic Resonance in Protein Folding Dynamics.

- Chemistry, Medicine
- Chemphyschem : a European journal of chemical physics and physical chemistry
- 2016

Although protein folding reactions are usually studied under static external conditions, it is likely that proteins fold in a locally fluctuating cellular environment in vivo. To mimic such behavior… Expand

Nonlinear resonance: Determining maximal autoresonant response and modulation of spontaneous otoacoustic emissions

- Physics
- 2011

Author: Carey Witkov Title: Nonlinear Resonance: Determining Maximal Autoresonant Response and Modulation of Spontaneous Otoacoustic Emissions Institution: Florida Atlantic University Dissertation… Expand

Efficient Iterative Methods for Solving the SIR Epidemic Model

- Mathematics
- 2021

In this article, the numerical and approximate solutions for the nonlinear differential equation systems, represented by the epidemic SIR model, are determined. The effective iterative methods,… Expand

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