Related papers: Statistical multi-moment bifurcations in random de…
The aim of this paper is to study the steady states of the mathematical models with delay kernels which describe pathogen-immune dynamics of many kinds of infectious diseases. In the study of mathematical models of infectious diseases it is…
Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing…
We develop a global Hopf bifurcation theory for differential equations with a state-dependent delay governed by an algebraic equation, using the $S^1$-equivariant degree. We apply the global Hopf bifurcation theory to a model of genetic…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…
We investigate the bifurcation phenomena for stochastic systems with multiplicative Gaussian noise, by examining qualitative changes in mean phase portraits. Starting from the Fokker-Planck equation for the probability density function of…
We study the time evolution of perturbations in spatially extended chaotic systems in the presence of quenched disorder. We find that initially random perturbations tend to exponentially localize in space around static pinning centers that…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
In this paper, we investigate the dynamical behaviors of a delayed lateral vibration model of footbridges proposed based on the facts that pedestrians will reduce their walking speed or stop walking when the response of the footbridge…
In the presented paper a family of angiogenesis models, that is a generalisation of Hahnfeldt et al. model is proposed. Considered family of models is a system of two differential equations with distributed time delays. The global existence…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
A delayed differential equation modelling a single neuron with inertial term is considered in this paper. Hopf bifurcation is studied by using the normal form theory of retarded functional differential equations. When adopting a…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…
We explore a diffusive predator-prey system that incorporates the fear effect in advective environments. Firstly, we analyze the eigenvalue problem and the adjoint operator, considering Constant-Flux and Dirichlet (CF/D) boundary…
We study delay-induced transitions in consensus dynamics on signed networks with a ring topology. The proposed model is formulated as a system of delay differential equations incorporating both cooperative and antagonistic interactions, as…
Sudden and abrupt changes can occur in a nonlinear system within many fields of science when such a system crosses a tipping point and rapid changes of the system occur in response to slow changes in an external forcing. These can occur…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…