Classical canard explosion results in smooth systems require the vector field to be at least C, since canard cycles are created as the result of a Hopf bifurcation. The work on canards in nonsmooth, planar systems is recent and has thus far been restricted to piecewise-linear or piecewise-smooth Van der Pol systems, where an extremum of the critical manifold arises from the nonsmoothness. In bo...

This paper provides a global picture of the bifurcation scenario of the Hindmarsh-Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurc...

Recently, there has been an interest in designing systems that employ buckling bifurcation as a desired mechanism to generate motion and/or form. As buckling has traditionally been considered a failure mode to be avoided, computational tools for predicting the state of the system after buckling are not well developed. For example, modules for post-bifurcation studies are not available in most o...

Prominent changes in neuronal dynamics have previously been attributed to a specific switch in onset bifurcation, the Bogdanov-Takens (BT) point. This study unveils another, relevant and so far underestimated transition point: the saddle-node-loop bifurcation, which can be reached by several parameters, including capacitance, leak conductance, and temperature. This bifurcation turns out to indu...

In this paper we present a registration method for cerebral vascular structures in the 2D MRA images. The method is based on bifurcation structures. The usual registration methods, based on point matching, largely depend on the branching angels of each bifurcation point. This may cause multiple feature correspondence due to similar branching angels. Hence, bifurcation structures offer better re...

An aneurysm involved in common carotid artery (CCA) bifurcation is a rare clinical condition. There are not enough natural follow-up data, and there is no evidence-based treatment algorithm [1]. An endovascular approach is used to treat CCA bifurcation aneurysms, as it offers some advantages in selected patient populations; nonetheless, closure of the aneurysmal segment in CCA bifurcation using...

Stationary Bloch waves are considered in the Gross-Pitaevskii equation with a periodic potential for varying strengths of inter-atomic interactions. Upon a sufficient increase of the inter-atomic interactions one may observe a bifurcation in the number and stability of stationary states. This bifurcation generates loops in the energy bands of the Bloch waves near the ends and the center of the ...

Traveling wavetrains in generalized two–species predator–prey models and two– component reaction–diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual ”spatial” variable) is considered. For general functional forms of the nonlinear prey birthrate/prey deathrate or reaction terms, a Hopf bifurcation is shown to occur at two different criti...

In this paper, a mathematically rigorous analysis for bifurcation structure of a spatially uniform stationary solution in nonlinear Schrödinger equations with a cubic nonlinearity and a dissipation, and with a detuning term is presented. Numerically, it has been reported that the “snake bifurcation” occurs, but this equation does not have the variational (Hamiltonian) structure. Therefore, both...

Information processing in the brain crucially depends on encoding properties of single neurons, with particular relevance of the spike-generation mechanism. The latter hinges upon the bifurcation type at the transition point between resting state and limit cycle spiking. Prominent qualitative changes in encoding have previously been attributed to a specific switch of such a bifurcation at the B...