In this paper, flip bifurcations of homoclinic orbits in conservative reversible systems are analysed. In such systems, orbit-flip and inclination-flip bifurcations occur simultaneously. It is shown that multi-pulses either do not bifurcate at all at flip bifurcation points or else bifurcate simultaneously to both sides of the bifurcation point. An application to a fifth-order model of water wa...

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...

This study aims to classify the critical points of functions with 4 variables and 8 parameters, we found caustic for certain function spreading points. Finally, as an application, bifurcation solutions equation sixth order boundary conditions using Lyapunov-Schmidt method in variational case.

In this work we present a washout filter based control approach for stabilizing the oscillations in HodgkinHuxley type neurons. The oscillations occur due to the bifurcations that arise from the potassium and sodium channel conductance deviations. The MATCONT toolbox software environment was used for analysis of the bifurcation points in conjunction with MATLAB. The simulations of the Hodgkin-H...

q{phase transition points in the context of the thermodynamical formalism of dy-namical systems arise via the degeneracy of eigenvalues of the corresponding transfer operator. The scaling behaviour near bifurcation points of dynamical systems is investigated by a mean eld like expansion for the characteristic equation of this operator. Scaling relations in the vicinity of q{phase transition poi...

A fingerprint matching is a very difficult problem. Minutiae-based-matching is the most popular and widely used technique for fingerprint matching. The minutiae points considered in automatic identification systems are based normally on termination and bifurcation points. In this paper we propose a new technique for fingerprint matching using minutiae points and genetic programming. The goal of...

The classical pitchfork of singularity theory is a twice-degenerate bifurcation that typically occurs in dynamical system models exhibiting Z2 symmetry. Nonclassical pitchfork singularities also occur in many non-symmetric systems, where the total bifurcation environment is usually more complex. In this paper threedimensional manifolds of critical points, or limit-point shells, are introduced b...

In this paper we demonstrate the power of the computer algebra package conley, which enables one to compute connection and transition matrices, two of the main algebraic tools of the Conley index theory. In particular, we study the Cahn-Hilliard equation on the unit square and extend the results obtained in [Maier-Paape et al., 2007] to a bigger range of the bifurcation parameter. Besides provi...