A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this techn...

The recently developed short-time linear response algorithm, which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation, yields high precision of the response prediction. However, the computation of the shorttime linear response formula with the full rank tangent map can be expensive. Here we propose a numerical method to potentially overcome the...

In this paper we study the long time dynamics of solutions of Initial and Boundary Value Problem (IBVP) of the Korteweg-de Vries (hence-forth KdV) equation posed on a bounded domain: (*) . 0 , 0 ) , 1 ( , 0 ) , 1 ( ), ( ) , 0 ( , 0 , 1 0 ), ( ) 0 , ( , 0    > = = = > < < = = + + + t t u t u t h t u t x x x u u uu u u

The problem of forced magnetic reconnection in a resistive plasma is of fundamental interest for numerous laboratory and space plasma applications. Asymptotic solutions of a model of forced reconnection, originally proposed by J.B. Taylor, have been discussed in Refs. [1-3]. In a recent paper [4], Ishizawa and Tokuda (hereafter, IT) claim that previous analyses [1-3] of the Taylor problem are w...

The development of a sensor that can measure balance during quiet standing and predict stepping response in the event of perturbation has many clinically relevant applications, including closed-loop control of a neuroprothesis for standing. This study investigated the feasibility of an algorithm that can predict in real-time when an able-bodied individual who is quietly standing will have to ma...

We exhibit non-unique Leray solutions of the forced Navier-Stokes equations with hypodissipation in two dimensions. Unlike constructed \cite{albritton2021non}, we construct live at a supercritical scaling, which formally becomes negligible as $t \to 0^+$. In this it is possible to perturb Euler non-uniqueness scenario Vishik \cite{Vishik1,Vishik2} hypodissipative setting nonlinear level. Our pe...

here, a new method called aboodh transform homotopy perturbation method(athpm) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and aboodh transformto investigate some nonlinear partial dierential equations. the nonlinearterms can be handled by the use of homotopy perturbation method. the resultsshow the eciency of this...

We consider a class of semi-linear differential Volterra equations with memory terms, polynomial nonlinearities and random perturbation. For broad nonlinearities, we show that the system in concern admits unique weak solution. Also, any statistically steady state must possess regularity compatible Moreover, if sufficiently many directions are stochastically forced, employ generalized coupling a...

Perturbation of the laminar boundary layer by free-stream travelling waves was shown to produce highly-localized skin friction modification via steady streaming. The forced flow calculated numerically and studied as a function phase speed, frequency amplitude perturbations. Upstream-travelling always produced negative streaming, whereas downstream-travelling positive or streaming that varied wi...