Related papers: Backward bifurcation underlies rich dynamics in si…
The mathematical analysis of a three-tiered food-web describing anaerobic chlorophenol mineralisation has suggested the emergence of interesting dynamical behaviour through its specific ecological interactions, which include competition,…
We introduce a versatile class of prototype dynamical systems for the study of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling bifurcations and…
The paper presents bifurcation behavior of a single phase induction motor. This paper also attempts to discuss the bifurcation behavior of the system based on the evolution of different state variables. The bifurcation diagrams drawn…
Biofilament-motor protein complexes are ubiquitous in biology and drive the transport of cargo vital for many fundamental cellular processes. As they move, motor proteins exert compressive forces on the filaments to which they are attached,…
We study the dynamics of belief formation on multiple interconnected topics in networks of agents with a shared belief system. We establish sufficient conditions and necessary conditions under which sustained oscillations of beliefs arise…
Bifurcations of dynamical systems, described by a second order differential equations and by an impact condition are studied. It is shown that the variation of parameters when the number of impacts of a periodic solution increases, leads to…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
We perform one and two-parameter numerical bifurcation analysis of a mechanotransduction model approximating the dynamics of mesenchymal stem cell differentiation into neurons, adipocytes, myocytes and osteoblasts. For our analysis, we use…
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…
The role of cooperative effects (i.e. synergy) in transmission of infection is investigated analytically and numerically for epidemics following the rules of Susceptible-Infected-Susceptible (SIS) model defined on random regular graphs.…
Complex systems such as ecosystems, electronic circuits, lasers or chemical reactions can be modelled by dynamical systems which typically experience bifurcations. Transients typically suffer extremely long delays at the vicinity of…
Changes in the parameters of dynamical systems can cause the state of the system to shift between different qualitative regimes. These shifts, known as bifurcations, are critical to study as they can indicate when the system is about to…
We investigate a typical aerofoil section under dynamic stall conditions, the structural model is linear and the aerodynamic loading is represented by the Leishman-Beddoes semi-empirical dynamic stall model. The loads given by this model…
A piecewise-linear model with a single degree of freedom is derived from first principles for a driven vertical cantilever beam with a localized mass and symmetric stops. The resulting piecewise-linear dynamical system is smoothed by a…
The saddle-node bifurcation is the simplest example of a generic bifurcation in smooth ordinary differential equations, and is associated with the creation or destruction of a pair of equilibria. In this paper we examine the unfolding of…
The attractors of a dynamical system govern its typical long-term behaviour. The presence of many attractors is significant as it means the behaviour is heavily dependent on the initial conditions. To understand how large numbers of…
We identify two rather novel types of (compound) dynamical bifurcations generated primarily by interactions of an invariant attracting submanifold with stable and unstable manifolds of hyperbolic fixed points. These bifurcation types -…
Various biological phenomena, like cell differentiation and pattern formation in multicellular organisms, are explained using the bifurcation theory. Molecular network motifs like positive feedback and mutual repressor exhibit bifurcation…
There has been interest in the interactions between infectious disease dynamics and behaviour for most of the history of mathematical epidemiology. This has included consideration of which mathematical models best capture each phenomenon,…