Related papers: Oscillations in a white blood cell production mode…
We prove that the famous diffusive Brusselator model can support more complicated spatial-temporal wave structure than the usual temporal-oscillation from a standard Hopf bifurcation. In our investigation, we discover that the diffusion…
In this paper, we consider the nonlinear dynamical behaviors of some tabu leaning neuron models. We first consider a tabu learning single neuron model. By choosing the memory decay rate as a bifurcation parameter, we prove that Hopf…
Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay…
It is known that Lotka - Volterra type differential equations with delays or distributed delays have an important role in modeling ecological systems. In this paper we study the effects of distributed delay on the dynamics of the harvested…
In this paper, we study degenerate Hopf bifurcations in a class of parametrized retarded functional differential equations. Specifically, we are interested in the case where the eigenvalue crossing condition of the classical Hopf…
We provide an analytical proof of the existence of a stable periodic orbit contained in the region of coexistence of the three species of a tritrophic chain. The method used consists in analyzing a triple Hopf bifurcation. For some values…
Biological evolution has endowed the plant Arabidopsis thaliana with genetically regulated circadian rhythms. A number of authors have published kinetic models for these oscillating chemical reactions based on a network of interacting…
Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we…
In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is…
The impact of cell segregation and margination in blood disorders on microcirculatory hemodynamics within bifurcated vessels are physiologically significant, yet poorly understood. This study presents a comprehensive computational…
We consider a delay differential equation that occurs in the study of chronic myelogenous leukemia. After shortly reminding some previous results concerning the stability of equilibrium solutions, we concentrate on the study of stability of…
We study analytically and numerically the noise-induced transition between an absorbing and an oscillatory state in a Duffing oscillator subject to multiplicative, Gaussian white noise. We show in a non-perturbative manner that a stochastic…
We describe some families of differentiable vector fields with the Hopf bifurcation at infinity, without assuming the continuous differentiability. These vector fields have isolated singular points on the plane, and the initial families are…
We study bifurcation for the constant scalar curvature equation along a one-parameter family of Riemannian metrics on the total space of a harmonic Riemannian submersion. We provide an existence theorem for bifurcation points and a…
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 synthetic construction of intracellular circuits is frequently hindered by a poor knowledge of appropriate kinetics and precise rate parameters. Here, we use generalized modeling (GM) to study the dynamical behavior of topological…
Bifurcations leading to complex dynamical behaviour of non-linear systems are often encountered when the characteristics of feedback circuits in the system are varied. In systems with many unknown or varying parameters, it is an…
Hamiltonian bifurcations in the context of noncanonical Hamiltonian matter models are described. First, a large class of 1 + 1 Hamiltonian multi-fluid models is considered. These models have linear dynamics with discrete spectra, when…
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…
Herewith we discuss a network model of the ferroptosis avascular and vascular tumor growth based on our previous proposed framework. Chiefly, ferroptosis should be viewed as a first order phase transition characterized by a supercritical…