相关论文: Imperfect Homoclinic Bifurcations

Basic multimode impedance analysis grounded in the availability of nonequilibrium charge carriers and their retarded path towards equilibrium is used to access the inadequacy of equivalent circuits in nonlinear systems with inherent memory.…

Electromigration, a significant lifetime reliability concern in highperformance integrated circuits, is projected to grow even more important in future heterogeneously integrated systems that will service higher current loads. Today, EM…

We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the…

Metamaterials serve as versatile platforms for demonstrating condensed matter physics and non-equilibrium phenomena, with electrical circuits emerging as a particularly compelling medium. This review highlights recent advances in the…

We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…

It is shown that electron backscattering can enhance high-harmonic generation in periodic systems with broken translational symmetry. Paradigmatically, we derive for a finite chain of atoms the harmonic cutoff due to electrons backscattered…

A nonlinear electronic circuit comprising of three nodes with a feedback loop is analyzed. The system has two stable states, a uniform state and a sinusoidal oscillating state, and it transitions from one to another by means of a Hopf…

There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…

Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…

In this paper we complete the global qualitative analysis of a quartic ecological model. In particular, studying global bifurcations of singular points and limit cycles, we prove that the corresponding dynamical system has at most two limit…

The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…

Tunnelling from a chaotic potential well is explained in terms of a set of complex periodic orbits which contain information about the real dynamics inside the well as well as the complex dynamics under the confining barrier. These orbits…

We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \times Z_2$ symmetry. The rich…

The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the…

Closed-orbit theory provides a general approach to the semiclassical description of photo-absorption spectra of arbitrary atoms in external fields, the simplest of which is the hydrogen atom in an electric field. Yet, despite its apparent…

Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…

The inequations of the delays of the asynchronous circuits are written, by making use of pseudo-Boolean differential calculus. We consider these efforts to be a possible starting point in the semi-formalized reconstruction of the digital…

We perform experiments and phase model simulations with a ring network of oscillatory electrochemical reactions to explore the effect of random connections and non-isochronocity of the interactions on the pattern formation. A few additional…

Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…

Various biological phenomena, like cell differentiation and pattern formation in multicellular organisms, are explained using the bifurcation theory. Molecular network motifs like positive feedback and mutual repressor exhibit bifurcation…