Related papers: A classification of explosions in dimension one
We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis…
We suggest that superbursts from some low mass X-ray binaries may be due to breaking and re-formation of diquark pairs, on the surface of realistic strange stars. Diquarks are expected to break up due to the explosion and shock of the…
The Takens-Bogdanov bifurcation is a codimension two bifurcation that provides a key to the presence of complex dynamics in many systems of physical interest. When the system is translation-invariant in one spatial dimension with no…
As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit undergoes a bifurcation when it collides with a surface where the system is discontinuous. Under certain conditions this is a grazing-sliding bifurcation.…
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…
Motivated by the string landscape, inflation may happen on a high dimensional complicated potential. We propose a new way to construct some high dimensional random potentials, and study inflation on top of that, for up to 50-dimensions in…
The phenomenon of time resonances (or explosions) can explain the exponential reduction of the energy, which is accompanied for the certain degree by slight fluctuations under some conditions in the range of the energy strongly overlapped…
It was established in 2006 that bifurcations of three-dimensional diffeomorphisms with a homoclinic tangency to a saddle-focus fixed point with the Jacobian equal to 1 can lead to Lorenz-like strange attractors. In the present paper we…
The conjugate locus of a point $p$ in a surface $\mathcal{S}$ will have a certain number of cusps. As the point $p$ is moved in the surface the conjugate locus may spontaneously gain or lose cusps. In this paper we explain this…
The main objective of this article is to study the three-dimensional Rayleigh-Benard convection in a rectangular domain from a pattern formation perspective. It is well known that as the Rayleigh number crosses a critical threshold, the…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
In our previous work, it was shown that the topology of an event horizon (EH) is determined by the past endpoints of the EH. A torus EH (the collision of two EH) is caused by the two-dimensional (one-dimensional) set of the endpoints. In…
We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a…
We discuss the recently measured event-by-event multiplicity fluctuations in relativistic heavy-ion collisions. It is shown that the observed non-monotonic behaviour of the scaled variance of multiplicity distribution as a function of…
Macroevolutionary dynamics often display sudden, explosive surges, where systems remain relatively stable for extended periods before experiencing dramatic acceleration that frequently exceeds traditional exponential growth. This pattern is…
Black holes are the densest form of energy, and in the presence of compact dimensions black objects may take one of several forms including the black-hole and the black-string, the simplest relevant background being R^{3+1} * S^1. Recent…
Complex fission phenomena are studied in a unified way. Very general reflection asymmetrical equilibrium (saddle point) nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain…
We revisit here the dynamics of an engineered dimer granular crystal under an external periodic drive in the presence of dissipation. Earlier findings included a saddle-node bifurcation, whose terminal point initiated the observation of…
A number of physical processes show some form of bifurcation or periodic splintering of a single distribution into two new ones. Recently, it has been noted that cavity searches for interactions between photons and exotic fields may also…
We show that only considering the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation our models obtain Gaussian cluster distributions and compact clusters as…