We study a plethora of chaotic phenomena in the Hindmarsh-Rose neuron model with the use of several computational techniques including the bifurcation parameter continuation, spike-quantification, and evaluation of Lyapunov exponents in bi-parameter diagrams. Such an aggregated approach allows for detecting regions of simple and chaotic dynamics, and demarcating borderlines-exact bifurcation cu...

In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...

Two dynamical models that have been proposed for determining aspects of confined plasma behavior around L–H transitions are analysed using singular-ity theory and stability theory. The recognition problem for the unperturbed bifurcation sets is solved by applying singularity theory methods to determine the normal form and codimension of the singular points. We find that in both cases the unpert...

We examine the presence of general (nonlinear) time-independent Lie point symmetries in dynamical systems, and especially in bifurcation problems. A crucial result is that center manifolds are invariant under these symmetries: this fact, which may be also useful for explicitly nding the center manifold, implies that Lie point symmetries are inherited by the "reduced" bifurcation equation (a res...

We numerically compute solutions to the vector Ginzburg-Landau equation with a triple-well potential. We use the Galerkin Newton Gradient Algorithm of Neuberger & Swift and bifurcation techniques to find solutions. With a small parameter, we find a Morse index 2 triple junction solution. This is the solution for which Flores, Padilla, & Tonegawa gave an existence proof. We classify all of the s...

conclusion both techniques provided quantitatively consistent results of in vivo velocity vector fields in right internal carotid artery (rca). pc mri represented a good estimation of main flow patterns inside the vasculature, which seems to be acceptable for clinical use. however, limitations of each technique should be considered while interpreting results. subjects and methods mr imaging was...

In this paper, we introduce a two-strain SIR epidemic model with viral mutation and vaccine administration. We discuss analyze the existence stability of equilibrium points. This has three types points, namely disease-free equilibrium, dominance point strain two, coexistence endemic point. The local two are verified by using Routh--Hurwitz criteria, while for global used suitable Lyapunov funct...