Related papers: Stabilized rapid oscillations in a delay equation:…
We consider optimization problems associated to a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizing $T$-cycles of…
One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations…
This manuscript deals with the stability and bifurcation analysis of the equation $D^{2\alpha}x(t)+c D^{\alpha}x(t)=a x(t)+b x(t-\tau)$, where $0<\alpha<1$ and $\tau>0$. We sketch the boundaries of various stability regions in the parameter…
We consider the model of economic growth with time delayed investment function. Assuming the investment is time distributed we can use the linear chain trick technique to transform delay differential equation system to equivalent system of…
We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast…
The spiking properties of a subcritical Hopf oscillator with a time delayed nonlinear feedback is investigated. Finite time delay is found to significantly affect both the statistics and the fine structure of the spiking behavior. These…
Bursting is a periodic transition between a quiescent state and a state of repetitive spiking. The phenomenon is ubiquitous in a variety of neurophysical systems. We numerically study the dynamical properties of a normal form of subcritical…
This paper focuses on the delay induced Hopf bifurcation in a dual model of Internet congestion control algorithms which can be modeled as a time-delay system described by a one-order delay differential equation (DDE). By choosing…
A Hopf bifurcation theorem is established for the abstract evolution equation $\frac{\mathrm{d}x}{\mathrm{d}t}=F(x,\lambda)$ in infinite dimensions under the degeneracy condition $Re \mu ^{\prime}(\lambda_0)= 0$ and suitable assumptions.…
For controlling periodic orbits with delayed feedback methods the periodicity has to be known a priori. We propose a simple scheme, how to detect the period of orbits from properties of the control signal, at least if a periodic but…
We present a novel scheme to stabilize high-frequency domain oscillations in semiconductor superlattices by a time-delayed feedback loop. Applying concepts from chaos control theory we propose to control the spatio-temporal dynamics of…
We study the stability of unstable steady states in scalar retarded time-delayed systems subjected to a variable-delay feedback control. The important aspect of such a control problem is that time-delayed systems are already…
The relay autotuning method identifies plant parameters, from oscillations of the plant under relay feedback. To predict the presence and nature of such oscillations, we apply the following two approaches: (a) analysis of the switching…
This paper generalizes the existing minimal model of the hypothalamic-pituitary-adrenal (HPA) axis in a realistic way, by including memory terms: distributed time delays, on one hand and fractional-order derivatives, on the other hand. The…
We report on a significant improvement of the classical time-delayed feedback control method for stabilization of unstable periodic orbits or steady states. In an electronic circuit experiment we were able to realize time-varying and…
In the first part of this article, we study feedback stabilization of a parabolic coupled system by using localized interior controls. The system is feedback stabilizable with exponential decay $-\omega<0$ for any $\omega>0$. A stabilizing…
We study synchronization in delay-coupled oscillator networks, using a master stability function approach. Within a generic model of Stuart-Landau oscillators (normal form of super- or subcritical Hopf bifurcation) we derive analytical…
Autonomous sustained oscillations are ubiquitous in living and nonliving systems. As open systems, far from thermodynamic equilibrium, they defy entropic laws which mandate convergence to stationarity. We present structural conditions on…
We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…
Feedback delay has been identified as a key ingredient in the quorum sensing synchronization of synthetic gene oscillators. While this influence has been evidenced at the theoretical level in a simplified system of degrade-and-fire…