Related papers: Bifurcations and Chaos in Time Delayed Piecewise L…
In this paper we present an approach in which synchronization of chaos is used to address identification problems. In particular, we are able to identify: (i) the discontinuity points of systems described by piecewise dynamical equations…
This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the…
The Takens-Bogdanov bifurcation is a codimension two bifurcation that provides a key to the presence of complex dynamics in many systems of physical interest. When the system is translation-invariant in one spatial dimension with no…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…
We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…
Linear conjugacy offers a new perspective to broaden the scope of stable biochemical reaction networks to the systems linearly conjugated to the well-established complex balanced mass action systems ($\ell$cCBMASs). This paper addresses the…
Using the predictor-corrector scheme, the fractional order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional order diffusionless system for variation of the single control parameter is…
Noise play a creative role in the evolution of periodic and complex systems which are essential for continuous performance of the system. The interaction of noise generated within one component of a chaotic system with other component in a…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodically [Phys. Rev. Lett. 120, 084102 (2018)] and quasiperiodically [Phys. Rev. E 107, 014205 (2023)] time-varying delay. Compared to…
A class of discrete-time nonlinear positive time-delay switched systems with sector-type nonlinearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov--Krasovskii functionals for this system…
We report on a novel behavior of solitary localized structures in a real Swift-Hohenberg equation subjected to a delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to nontrivial…
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…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
We show that a simple piecewise-linear system with time delay and periodic forcing gives rise to a rich bifurcation structure of torus bifurcations and Arnold tongues, as well as multistability across a significant portion of the parameter…
This article proposes a non-autonomous mathematical model with delay for confrontation between two countries, and examines the stability of its equilibrium state. Our criteria for stability take into account the influence of the factor of…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
The transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered. It is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control…