相关论文: Stabilizing unstable periodic orbits in the Lorenz…

The problem of stabilization of unstable periodic orbits of discrete nonlinear systems is considered in the article. A new generalization of the delayed feedback, which solves the stabilization problem, is proposed. The feedback is…

Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles traversing a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of the Classical…

We derive the normal form for the delay-induced Hopf bifurcation in the first-order phase-locked loop with time delay by the multiple scaling method. The resulting periodic orbit is confirmed by numerical simulations. Further detailed…

In this paper we perform the parameter-dependent center manifold reduction near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf and transcritical-Hopf bifurcations in delay differential equations (DDEs). This allows us to initialize the…

We prove an analytical limitation on the use of time-delayed feedback control for the stabilization of periodic orbits in autonomous systems. This limitation depends on the number of real Floquet multipliers larger than unity, and is…

Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is…

We consider the scalar delay differential equation $$ \dot{x}(t)=-x(t)+f_{K}(x(t-1)) $$ with a nondecreasing feedback function $f_{K}$ depending on a parameter $K$, and we verify that a saddle-node bifurcation of periodic orbits takes place…

The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to…

Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been modeled by a system of ordinary differential equations based on the uptake of zinc, expression of a transporter protein and the interaction between an activator…

The normal forms up to the third order for a Hopf-steady state bifurcation of a general system of partial functional differential equations (PFDEs) is derived based on the center manifold and normal form theory of PFDEs. This is a…

We study the two state model which describes the balance equation for carbon dioxide and oxygen. These are nonlinear parameter dependent and because of the transport delay in the respiratory control system, they are modeled with delay…

We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…

A 1:2 internally resonant mechanical system can undergo secondary Hopf (Neimark-Sacker) bifurcations, resulting in a quasi-periodic response when the system is subject to harmonic excitation. While these quasi-periodic orbits have been…

Hysteresis phenomena and multistability play crucial roles in the dynamics of coupled oscillators, which are now interpreted from the point of view of codimension-two bifurcations. On the Ott-Antonsen's manifold, complete bifurcation sets…

Using the model of a generalized Van der Pol oscillator in the regime of subcritical Hopf bifurcation we investigate the influence of time delay on noise-induced oscillations. It is shown that for appropriate choices of time delay either…

The purpose of this article is to introduce the original results which devoted with the nonlinear control system problems involves of nonlinear differential equations of fractional orders. Thus, this system is described with a mixed of…

In this paper, the dynamics of a modified Leslie-Gower predator-prey system with two delays and diffusion is considered. By calculating stability switching curves, the stability of positive equilibrium and the existence of Hopf bifurcation…

This paper pursues the study carried out by the authors in "Stability and Hopf bifurcation in a hexagonal governor system", focusing on the codimension one Hopf bifurcations in the hexagonal Watt governor differential system. Here are…

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…

We implement the geometric method proposed in ([9], [3], [16]) to analytically predict the sequence of bifurcations leading to a change of stability and/or the appearance of new periodic orbits in the secular 3D planetary three body…