Self-sustained oscillations with delayed velocity feedback

Patterns of Sustained Oscillations in Neural Networks with Delayed Interactions

We study the Cohen-Grossberg-Hopfield model of neural networks with delayed interactions when the interconnection matrix has only real and purely imaginary eigenvalues. Two indices, the symmetry index and the antisymmetry index, are introduced and are used to describe the pattern of sustained oscillations caused by the delay. It is shown that the parameter plane of these indices is divided into...

Self-Sustained Oscillations of Nonlinearly Viscoelastic Layers

Control of noise-induced oscillations by delayed feedback

We propose a method to control noise-induced motion, based on using delayed feedback in the form of the difference between the delayed and the current states of the system. The method is applied to two different types of systems, namely, a selfoscillator near Andronov-Hopf bifurcation and a threshold system. In both cases we demonstrate that by variation of time delay one can effectively contro...

Synchronization of noise-induced oscillations by time-delayed feedback

Abstract. We consider two mutually coupled neural populations represented by two FitzHughNagumo systems prepared at parameter values at which no autonomous oscillations occur. Each system is driven by its own source of random fluctuations realized by Gaussian white noise. We show that an extended time-delayed feedback scheme is able to influence the global cooperative dynamics of the ensemble o...

Delayed-feedback control of oscillations in non-linear planar systems

The use of delayed feedback of position for the control of oscillatory behaviour is analysed. It is shown that linear feedback can annihilate limit cycles and stabilize the origin. Furthermore, it is possible to create an asymptotically stable limit cycle with any prescribed amplitude using a simple nonlinear feedback. For almost all values of the delay, these feats can be achieved without usin...