Related papers: Imperfect Homoclinic Bifurcations
We classify the local bifurcations of one dov quantum billiards, showing that only saddle-center bifurcations can occur. We analyze the resulting planar system when there is no coupling in the superposition state. In so doing, we also…
We present the first observations of cylindrical symmetry breaking in highly excited diamagnetic hydrogen with a small crossed electric field, and we give a semiclassical interpretation of this effect. As the small perpendicular electric…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
Multicritical Ising models and their perturbations are paradigmatic models of statistical mechanics. In two space-time dimensions, these models provide a fertile testbed for investigation of numerous non-perturbative problems in…
The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system…
Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…
The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…
We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions…
Techniques like speckle holography and shearography are rarely applied due to the complexity of instrument setup and lack of automated result analysis, despite their potential. By simulating speckle interferometric outcomes, we seek to…
The extraction of transition frequencies from a spectrum has conventionally relied on empirical methods, and particularly in complex systems, it is a time-consuming and cumbersome process. To address this challenge, we establish a…
We investigate planar piecewise-smooth vector fields with a discontinuity line, focusing on the bifurcation of crossing limit cycles that arise when one of the vector fields is translated along the discontinuity set. We establish…
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
We characterize the graphs $G$ for which their toric ideals $I_G$ are complete intersections. In particular we prove that for a connected graph $G$ such that $I_G$ is complete intersection all of its blocks are bipartite except of at most…
For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via…
Acoustically excited bubbles are involved in a wide range of phenomena and applications ranging from oceanography to sonoluminescence; they have applications in chemistry, medical imaging, and therapeutic ultrasound. The complexity of…
The global many-electron wave function overlap matrix accounts for all effects beyond the Born-Oppenheimer approximation in the discrete variable local diabatic representation, a numerically exact framework for modeling nonadiabatic conical…
The dynamics of globally coupled map lattices can be described in terms of a nonlinear Frobenius--Perron equation in the limit of large system size. This approach allows for an analytical computation of stationary states and their…
The direct observation of non-adiabatic dynamics at conical intersections is a long-standing goal of molecular physics. Novel time-resolved spectroscopies have been proposed which are sensitive to electronic coherences induced by the…