Related papers: Hopf bifurcation analysis of pathogen-immune inter…
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…
A major contribution to the onset and development of autoimmune disease is known to come from infections. An important practical problem is identifying the precise mechanism by which the breakdown of immune tolerance as a result of immune…
In this paper, we study the structure and dynamical properties of protein contact networks with respect to other biological networks, together with simulated archetypal models acting as probes. We consider both classical topological…
A ferrofluid droplet confined in a Hele-Shaw cell can be deformed into a stably spinning ``gear,'' using crossed magnetic fields. Previously, fully nonlinear simulation revealed that the spinning gear emerges as a stable traveling wave…
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…
The spatiotemporal patterns of a reaction diffusion mussel-algae system with a delay subject to Neumann boundary conditions is considered. The paper is a continuation of our previous studies on delay-diffusion mussel-algae model. The global…
In this paper, an attempt has been made to understand the parametric excitation of a periodic orbit of nonlinear oscillator which can be a limit cycle, center or a slowly decaying center-type oscillation. For this a delay model is…
This article deals with an autonomous differential equation model that studies the interaction between the immune system and the growth of tumor cells with strong and weak Allee effects. The Allee effect refers to interspecific competition,…
In this paper, we analyse the celebrated Haken-Kelso-Bunz (HKB) model, describing the dynamics of bimanual coordination, in the presence of delay. We study the linear dynamics, stability, nonlinear behaviour and bifurcations of this model…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
In this paper, we present an algorithm for deriving the normal forms of Bautin bifurcations in reaction-diffusion systems with time delays and Neumann boundary conditions. On the center manifold near a Bautin bifurcation, the first and…
The equivariant Hopf bifurcation dynamics of a class of system of partial differential equations is carefully studied. The connections between the current dynamics and fundamental concepts in hyperbolic conservation laws are explained. The…
A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases…
A four-dimensional mathematical model of the hypothalamus-pituitary-adrenal (HPA) axis is investigated, incorporating the influence of the GR concentration and general feedback functions. The inclusion of distributed time delays provides a…
As offered by the World Health Organisation (WHO), close to half of the population in the world's resides in dengue-risk zones. Dengue viruses are transmitted to individuals by Aedes mosquito species infected bite (Ae. Albopictus of Ae.…
Protein phosphorylation cycles are important mechanisms of the post translational modification of a protein and as such an integral part of intracellular signaling and control. We consider the sequential phosphorylation and…
We study networks of theta neurons arranged on a ring with delayed interactions. In the continuum limit the systems are described by next generation neural field models with delays. We consider distributed delays with both finite and…
We investigate state dependent delay differential equations with distributed memory, combining discrete state dependent delays and a convolution type memory operator. Under Lipschitz type assumptions on the delay, kernel, and nonlinear…
In this paper, we consider a general single population model with delay and patch structure, which could model the population loss during the dispersal. It is shown that the model admits a unique positive equilibrium when the dispersal rate…
We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale separation. The framework is applicable to models where an…