Related papers: Delayed Feedback Control near Hopf Bifurcation
We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…
For a wide class of second order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal, allows to stabilize unstable motions…
Feedback optimisation is an emerging technique aiming at steering a system to an optimal steady state for a given objective function. We show that it is possible to employ this control strategy in a distributed manner. Moreover, we prove…
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…
Closed-loop or feedback control ratchets use information about the state of the system to operate with the aim of maximizing the performance of the system. In this paper we investigate the effects of a time delay in the feedback for a…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
A ferrofluid droplet confined in a Hele-Shaw cell can be deformed into a stably spinning ``gear,'' using crossed magnetic fields. Previously, fully nonlinear simulation revealed that the spinning gear emerges as a stable traveling wave…
We study the stability of the fixed-point solution of an array of mutually coupled logistic maps, focusing on the influence of the delay times, $\tau_{ij}$, of the interaction between the $i$th and $j$th maps. Two of us recently reported…
The present paper studies a feedback regulation problem, which may be interpreted as an adaptive control problem, but has not yet been studied in the control literature. The problem, which arises in at least two different biological…
This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…
We consider a one-dimensional controlled reaction-diffusion equation, where the control acts on the boundary and is subject to a constant delay. Such a model is a paradigm for more general parabolic systems coupled with a transport…
The delay logistic map with two types of q-deformations: Tsallis and Quantum-group type are studied. The stability of the map and its bifurcation scheme is analyzed as a function of the deformation and delay feedback parameters. Chaos is…
We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space…
We consider linear delay differential equations at the verge of Hopf instability, i.e. a pair of roots of the characteristic equation are on the imaginary axis of the complex plane and all other roots have negative real parts. When…
Effects of immune delay on symmetric dynamics are investigated within a model of antigenic variation in malaria. Using isotypic decomposition of the phase space, stability problem is reduced to the analysis of a cubic transcendental…
We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quantify the effect of delay through the buffering in the…
We study optimal proportional feedback controllers for spatially invariant systems when the controller has access to delayed state measurements received from different spatial locations. We analyze how delays affect the spatial locality of…
We consider a robust stabilization of the fourth-order oscillatory systems with non-collocated output sensing. Worth recalling is that the fourth-order systems are relatively common in mechatronics as soon as there are two-mass or more…
Diffusion-induced turbulence in spatially extended oscillatory media near a supercritical Hopf bifurcation can be controlled by applying global time-delay autosynchronization. We consider the complex Ginzburg-Landau equation in the…
Feedback controlled ratchets are thermal rectifiers that use information on the state of the system to operate. We study the effects of time delays in the feedback for a protocol that performs an instantaneous maximization of the…