Related papers: Universal bifurcation scenarios in delay-different…
The location of roots of the characteristic equation of a linear delay differential equation (DDE) determines the stability of the linear DDE. However, by its transcendency, there is no general criterion on the contained parameters for the…
We consider noise perturbations of delay differential equations (DDE) experiencing Hopf bifurcation. The noise is assumed to be exponentially ergodic, i.e. transition density converges to stationary density exponentially fast uniformly in…
Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…
The aim of this paper is to study global bifurcations of non-constant solutions of some nonlinear elliptic systems, namely the system on a sphere and the Neumann problem on a ball. We study the bifurcation phenomenon from families of…
We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classic differential equation models with…
We consider state-dependent delay equations (SDDE) obtained by adding delays to a planar ordinary differential equation with a limit cycle. These situations appear in models of several physical processes, where small delay effects are…
We study, by means of a topological approach, the forced oscillations of second order functional retarded differential equations subject to periodic perturbations. We consider a delay-type functional dependence involving a gamma probability…
A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function…
The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form for regular matrix pencil, a complete characterization of…
Bifurcation equations, non-degeneracy and transversality conditions are obtained for the fold, transcritical, pitchfork and flip bifurcations for periodic points of one dimensional implicitly defined discrete dynamical systems. The backward…
A recent work by the authors on the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in delay differential equations motivates the derivation of periodic normal forms. In this paper, we prove the…
The aim of this work is to investigate the qualitative behaviour of a financial dynamical system which contains a time delay. We investigate the dynamic response of this system of which variables are interest rate, investment demand, price…
The sunflower equation describes the motion of the tip of a plant due to the auxin transportation under the influence of gravity. This work proposes the fractional-order generalization to this delay differential equation. The equation…
We present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple model consisting of just two oscillators with a time delayed coupling, the bifurcation…
Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…
This study analyses the dynamical consequences of heterogeneous temporal delays within a quorum sensing-inspired (QS-inspired) system, specifically addressing the differential response kinetics of two sub-populations to signalling…
The bifurcation diagram of a model nonlinear Langevin equation with delayed feedback is obtained numerically. We observe both direct and oscillatory bifurcations in different ranges of model parameters. Below threshold, the stationary…
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…
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.…
We study the structure of the set of harmonic solutions to perturbed nonautonomous, T-periodic, separated variables ODEs on manifolds. The perturbing term is allowed to contain a finite delay and to be T-periodic in time.