Search results for "bifurcation"
showing 10 items of 204 documents
Perturbations of symmetric elliptic Hamiltonians of degree four
2006
AbstractIn this paper four-parameter unfoldings Xλ of symmetric elliptic Hamiltonians of degree four are studied. We prove that in a compact region of the period annulus of X0 the displacement function of Xλ is sign equivalent to its principal part, which is given by a family induced by a Chebychev system; and we describe the bifurcation diagram of Xλ in a full neighborhood of the origin in the parameter space, where at most two limit cycles can exist for the corresponding systems.
Chreod.
2020
The concept of chreod was introduced in 1957 by the English theoretical biologist Conrad Hal Waddington (cf. Waddington: 1957; Galperin: 2008). From a linguistic point of view, the word “chreod” is a neologism, or, more precisely, a compound formed by the combination of two Greek words: the verb chre- (“it is necessary, must”) and the substantive -hodos (“way, road”). Therefore, it means literally “obliged pathway” (cf. Fabris 2018: 252, n. 6). Of course, such an etymology covers only a little bit of the semantic repertoire deployed by chreod. But, it is however true that some aspects of the biology of living systems can be described in these terms. Indeed, at the most general level, the id…
Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems
2011
The method of harmonic linearization, numerical methods, and the applied bifurcation the- ory together discover new opportunities for analysis of oscillations of control systems. In the present survey analytical-numerical algorithms for hidden oscillation localization are discussed. Examples of hidden attrac- tor localization in Chua's circuit and counterexamples construction to Aizerman's conjecture and Kalman's conjecture are considered.
Heteroclinic contours and self-replicated solitary waves in a reaction–diffusion lattice with complex threshold excitation
2008
Abstract The space–time dynamics of the network system modeling collective behavior of electrically coupled nonlinear cells is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. Heteroclinic orbits defining traveling wave front solutions are investigated in a moving frame system. A heteroclinic contour formed by separatrix manifolds of two saddle-foci is found in the phase space. The existence of such structure indicates the appearance of complex wave patterns in the network. Such solutions have been confirmed and analyzed numerically. Complex homoclinic orbits found in the neighborhood of the heteroclinic contour define …
Active spike transmission in the neuron model with a winding threshold manifold
2012
International audience; We analyze spiking responses of excitable neuron model with a winding threshold manifold on a pulse stimulation. The model is stimulated with external pulse stimuli and can generate nonlinear integrate-and-fire and resonant responses typical for excitable neuronal cells (all-or-none). In addition we show that for certain parameter range there is a possibility to trigger a spiking sequence with a finite number of spikes (a spiking message) in the response on a short stimulus pulse. So active transformation of N incoming pulses to M (with M>N) outgoing spikes is possible. At the level of single neuron computations such property can provide an active "spike source" comp…
Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction
2020
We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Caratheodory terms. One is parametric, $$(p-1)$$-sublinear with a partially concave nonlinearity near zero. The other is $$(p-1)$$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $$\lambda >0$$ varies.
Bifurcations of Elementary Graphics
1998
After the regular limit periodic sets, the simplest limit periodic sets are the elementary graphics.
Pattern Formation During Dry Corrosion of Metals and Alloys
1987
About corrosion of metals and alloys, many exciting problems are not entirely solved. One of them concerns some morphological features such as, for example, stratified periodic structures that may appear, for example during the oxidation or sulfidation of metals and alloys. In this context, a high temperature corrosion kinetics is interpreted in terms of a bistable chemical system which can oscillate spontaneously if a feedback effect could exist. Some models analyse these patterning from a theoretical point of view. Stability analyses of the uniform standard steady state point out that it can be unstable by bifurcation and give rise to multilayered scales. Some non linearities, peculiar to…
Kinematic splitting algorithm for fluid–structure interaction in hemodynamics
2013
Abstract In this paper we study a kinematic splitting algorithm for fluid–structure interaction problems. This algorithm belongs to the class of loosely-coupled fluid–structure interaction schemes. We will present stability analysis for a coupled problem of non-Newtonian shear-dependent fluids in moving domains with viscoelastic boundaries. Fluid flow is described by the conservation laws with nonlinearities in convective and diffusive terms. For simplicity of presentation the structure is modelled by the generalized string equation, but the results presented in the paper may be generalized to more complex structure models. The arbitrary Lagrangian–Eulerian approach is used in order to take…
On the numerical solution of some finite-dimensional bifurcation problems
1981
We consider numerical methods for solving finite-dimensional bifurcation problems. This paper includes the case of branching from the trivial solution at simple and multiple eigenvalues and perturbed bifurcation at simple eigenvalues. As a numerical example we treat a special rod buckling problem, where the boundary value problem is discretized by the shooting method.