The bifurcation diagram corresponding to stationary solutions of the nonlinear Schrödinger equation describing a superflow around a disc is numerically computed using continuation techniques. When the Mach number is varied, it is found that the stable and unstable (nucleation) branches are connected through a primary saddle-node and a secondary pitchfork bifurcation. Computations are carried ou...

The focus of this study was to experimentally investigate the development of nonlinear cyclic dispersion patterns in spark ignition engines. The results indicated a transition from stochastic behavior to noisy nonlinear determinism as equivalence ratio was decreased to very lean conditions. The transition to nonlinear deterministic behavior appeared to occur via a period-doubling bifurcation se...

A Josephson tunnel junction which is rf driven near a dynamical bifurcation point can amplify quantum signals. However, the bifurcation point will exist robustly only if the electrodynamic environment of the junction meets certain criteria. We develop a general formalism for dealing with the nonlinear dynamics of a Josephson junction embedded in an arbitrary microwave circuit. We find sufficien...

In this paper, we focus on a ratio dependent predator–prey system with selfand cross-diffusion and constant harvesting rate. By making use of a brief stability and bifurcation analysis, we derive the symbolic conditions for Hopf, Turing and wave bifurcations of the system in a spatial domain. Additionally, we illustrate spatial pattern formations caused by these bifurcations via numerical examp...

The influence of fluid depth in a convection problem in which heating is nonuniform is studied. We consider a vessel that has at the bottom a temperature distribution which has Gaussian shape in the transversal direction and whose surface is open to the atmosphere. Coupled buoyancy and thermocapillary effects are taken into account. The results confirm a stationary bifurcation and a prelude of ...

Fractal dimensions have been frequently applied to generalize the complexity and drainage of particular stream networks. Certain techniques to calculate dimension have become particularly popular, specifically the Divider method, functional-box counting, and as a function between bifurcation and length ratios. The frequency and variability with which these techniques are applied creates discrep...

The axonal arbors of the different types of neocortical and thalamic neurons appear highly dissimilar when viewed in conventional 2D reconstructions. Nevertheless, we have found that their one-dimensional metrics and topologies are surprisingly similar. To discover this, we analysed the axonal branching pattern of 39 neurons (23 spiny, 13 smooth and three thalamic axons) that were filled intrac...

Recently, ratio-dependent predator–prey systems have been regarded by some researchers as being more appropriate for predator–prey interactions where predation involves serious searching processes. Due to the fact that every population goes through some distinct life stages in real-life, one often introduces time delays in the variables being modelled. The presence of time delay often greatly c...

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two ...