In this paper, we apply first and higher-order Euler discretizations to compare dynamic systems in discrete and continuous time. In addition, we stress the difference between backward and forward-looking approximations. Focussing on local bifurcations, we find that time representation is neutral and asymptotically neutral for models with saddle-node and Hopf bifurcations, respectively. Converse...

In the present paper we study certain characteristic features associated with bifurcations of chaos in a ®nite dimensional dynamical system ± Murali±Lakshmanan±Chua (MLC) circuit equation and an in®nite dimensional dynamical system ± one-way coupled map lattice (OCML) system. We characterize chaotic attractors at various bifurcations in terms of r n …q† ± the variance of ¯uctuations of coarse-g...

In this paper we study Arnold’s tongues in a Z2-symmetric electronic circuit. They appear in a rich bifurcation scenario organized by a degenerate codimension-three Hopf–pitchfork bifurcation. On the one hand, we describe the transition open-to-closed of the resonance zones, finding two different types of Takens–Bogdanov bifurcations (quadratic and cubic homoclinic-type) of periodic orbits. The...

This work presents a novel modeling paradigm of the dynamical negotiation between clients running TCP (Transmission Control Protocol) and routers with the RED (Random Early Detection) active queue management scheme. The basic aim of the modeling is to understand the inherent nonlinearity in the interaction and how it manifests itself in the parametric sensitivities observed in practice. The mod...

Gutzwiller's trace formula allows interpreting the density of states of a classically chaotic quantum system in terms of classical periodic orbits. It diverges when periodic orbits undergo bifurcations, and must be replaced with a uniform approximation in the vicinity of the bifurcations. As a characteristic feature, these approximations require the inclusion of complex " ghost orbits ". By stu...

We report on transcritical bifurcations of periodic orbits in nonintegrable two-dimensional Hamiltonian systems. We discuss their existence criteria and some of their properties using a recent mathematical description of transcritical bifurcations in families of symplectic maps. We then present numerical examples of transcritical bifurcations in a class of generalized Hénon-Heiles Hamiltonians ...

An overview of homoclinic and heteroclinic bifurcation theory for autonomous vector fields is given. Specifically, homoclinic and heteroclinic bifurcations of codimension one and two in generic, equivariant, reversible, and conservative systems are reviewed, and results pertaining to the existence of multi-round homoclinic and periodic orbits and of complicated dynamics such as suspended horses...

The electronic domain is highly nonlinear, hence it is valuable to study the nonlinear effect particularly the chaos and bifurcation. The present paper deals with the simulative analysis of nonlinear dynamics in the boost converter with the help of bifurcation diagrams. In this brief communication, the current through inductor (IL) was considered as state variable and reference current (IREF) w...

The multi–scale Frangi vesselness filter is an established tool in (retinal) vascular imaging. However, it cannot properly cope with crossings or bifurcations since it only looks for elongated structures. Therefore, we disentangle crossings/bifurcations via (multiple scale) invertible orientation scores and apply vesselness filters in this domain. This new method via scale–orientation scores pe...

The multi-scale Frangi vesselness filter is an established tool in (retinal) vascular imaging. However, it cannot properly cope with crossings or bifurcations since it only looks for elongated structures. Therefore, we disentangle crossings/bifurcations via (multiple scale) invertible orientation scores and apply vesselness filters in this domain. This new method via scale-orientation scores pe...