Resonant forcing of nonlinear systems of differential equations.

  title={Resonant forcing of nonlinear systems of differential equations.},
  author={Vadas Gintautas and Alfred W. H{\"u}bler},
  volume={18 3},
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
Optimal entrainment with smooth, pulse, and square signals in weakly forced nonlinear oscillators
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 problemExpand
Optimal Control and Synchronization of Dynamic Ensemble Systems
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
Nonlinear oscillators exhibit synchronization (injection-locking) to external periodic forcings, which underlies the mutual synchronization in networks of nonlinear oscillators. Despite its historyExpand
The conservation laws with Lie symmetry analysis for time fractional integrable coupled KdV–mKdV system
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.
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
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 openExpand
Global dynamics of Chua Corsage Memristor circuit family: fixed-point loci, Hopf bifurcation, and coexisting dynamic attractors
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 anExpand
Stochastic Resonance in Protein Folding Dynamics.
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 behaviorExpand
Nonlinear resonance: Determining maximal autoresonant response and modulation of spontaneous otoacoustic emissions
Author: Carey Witkov Title: Nonlinear Resonance: Determining Maximal Autoresonant Response and Modulation of Spontaneous Otoacoustic Emissions Institution: Florida Atlantic University DissertationExpand
Efficient Iterative Methods for Solving the SIR Epidemic Model
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


Resonant Forcing of Chaotic Dynamics
Abstract We study resonances of multidimensional chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response, that is, theExpand
Resonances of nonlinear oscillators.
  • Wargitsch, Hübler
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
It is found that aperiodic driving forces are most effective for large nonlinearity and small friction and this optimal control is stable for several important systems. Expand
Resonant forcing of multidimensional chaotic map dynamics.
It is shown that resonant forcing functions of chaotic systems decrease exponentially, where the rate equals the negative of the largest Lyapunov exponent of the unperturbed system and the optimal forcing decreases rapidly and is only as effective as a single-push forcing. Expand
Regular and Chaotic Dynamics
This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular toExpand
Consolidated expansions for estimating the response of a randomly driven nonlinear oscillator
We consider a nonlinear oscillator driven by random, Gaussian “noise.” The oscillator, which is damped and has linear and cubic terms in the restoring force, is often called the “Duffing Equation.”Expand
Resonances of chaotic dynamical systems.
  • Ruelle
  • Physics, Medicine
  • Physical review letters
  • 1986
It appears desirable to analyze the decay of correlation functions and the possible analyticity of power spectra for physical time evolutions, and for computer generated simple dynamical systems (non-Axiom-A in general). Expand
Scaling behavior of the maximum energy exchange between coupled anharmonic oscillators.
The maximum energy exchange of two harmonically coupled nonlinear oscillators is investigated and it is shown that the corresponding resonance curves have a universal shape and become broader and smaller when the amplitude-frequency coupling becomes large. Expand
Dynamics of oscillators with periodic dichotomous noise
The dynamics of bistable oscillators driven by periodic dichotomous noise is described. The stochastic differential equation governing the flow implies smooth trajectories between noise switchingExpand
Deterministic nonperiodic flow
Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified withExpand
Effect of dynamical traps on chaotic transport in a meandering jet flow.
The present paper phenomenologically explain a connection between dynamical, topological, and statistical properties of chaotic mixing and transport in the model flow in terms of dynamical traps, singular zones in the phase space where particles may spend an arbitrarily long but finite time. Expand