Related papers: Bifurcation of solutions to Hamiltonian boundary v…
Random diffeomorphisms with bounded absolutely continuous noise are known to possess a finite number of stationary measures. We discuss dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of…
We study the effect of changes in the parameters of a two-dimensional potential energy surface on the phase space structures relevant for chemical reaction dynamics. The changes in the potential energy are representative of chemical…
Local bifurcation theory typically deals with the response of a degenerate but isolated equilibrium state or periodic orbit of a dynamical system to perturbations controlled by one or more independent parameters, and characteristically uses…
Decision making is a fundamental capability of autonomous systems. As decision making is a process which happens over time, it can be well modeled by dynamical systems. Often, decisions are made on the basis of perceived values of the…
For piecewise-smooth ordinary differential equations, the occurrence of a Hopf bifurcation on a switching surface is known as a boundary Hopf bifurcation. Boundary Hopf bifurcations are codimension-two, so occur at points in two-parameter…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
Bifurcations of dynamical systems, described by a second order differential equations and by an impact condition are studied. It is shown that the variation of parameters when the number of impacts of a periodic solution increases, leads to…
The global bifurcation diagrams for two different one-parametric perturbations ($+\lambda x$ and $+\lambda x^2$) of a dissipative scalar nonautonomous ordinary differential equation $x'=f(t,x)$ are described assuming that 0 is a constant…
Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics, and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically…
An application of variational principle to bifurcation of periodic solution in Lagrangian mechanics is shown. A few higher derivatives of the action integral at a periodic solution reveals the behaviour of the action in function space near…
We give an account of the various changes in the stability character in the five types of Riemann ellipsoids by establishing the occurrence of different quasi-periodic Hamiltonian bifurcations. Suitable symplectic changes of coordinates,…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps which can not be classified among the generic cases like saddle-node, pitchfork or Hopf…
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…
Moment systems arise in a wide range of contexts and applications, e.g. in network modeling of complex systems. Since moment systems consist of a high or even infinite number of coupled equations, an indispensable step in obtaining a…
A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology…
A unified framework is proposed to quantitatively characterize pitchfork bifurcations and associated symmetry breaking in the elliptic restricted three-body problem (ERTBP). It is known that planar/vertical Lyapunov orbits and Lissajous…
We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal -- there are many technical details which are not fully discussed. The topics are chosen to…
The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise deterministic Markov processes arising from stochastic switching dynamics near fold,…
A bifurcation about the uniqueness of a solution of a singularly perturbed free boundary problem of phase transition associated with the p-Laplacian, subject to given boundary condition is proved in this paper. We show this phenomenon by…