In this paper, we investigate bifurcation processes for the mean eld theory (MFT) annealing applied to traveling salesman problems (TSPs). Due to the symmetries of the TSP free energy function, some special bifurcations occur: cyclic symmetry breaking bifurcations and reverse symmetry breaking bifurcations. Saddle-node bifurcations also occur. Which type of bifurcations occurs depends on the sy...

bifurcations leading to chaos have been investigated in a number of one dimensional dynamical systems by varying the parameters incorporated within the systems. the property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. in the process, the calculations for invariant set have also been carried out. a bro...

We study the phase reduction of two coupled van der Pol oscillators with asymmetric repulsive coupling under an external harmonic force. We show that the system of two phase oscillators undergoes a Hopf bifurcation and possesses multistability on a 2π-periodic phase plane. We describe the bifurcation mechanisms of formation of multistability in the phase-reduced system and show that the Androno...

A new method for investigation of X-ray beam propagation in a rough narrow dielectrical waveguide is proposed on the basis of the numerical integration of the quazioptical equation. In calculations a model rough surface is used with the given distribution of hights of roughness and given correlation properties of the surface. The method is free from the limitations such as infiniteness of the s...

Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps that cannot be classified among the generic cases like saddle-node, pitchfork, or Hopf bifurcations occurring in smooth maps. In this paper we first present experimental results to establish the need for the development of a theoretical framework and clas...

Abstract. We study the appearance of a novel phenomenon for linearly coupled identical bursters: synchronized bursts where there are changes of spike synchrony within each burst. The examples we study are for normal form elliptic bursters where there is a periodic slow passage through a Bautin (codimension two degenerate Andronov-Hopf) bifurcation. This burster has a subcritical Andronov-Hopf b...

Bifurcations observed in a phase converter circuit are investigated. We obtain a codimension two bifurcation which is intersection of period-doubling bifurcations. Periodic solutions generated by these bifurcations become chaotic states through a cascade of a codimension three bifurcation which is intersection of D-type of branching and period-doubling bifurcation.

The stick-slip dynamics of the peeling of an adhesive tape is characterized by bifurcations that have been experimentally well studied. In this work, we investigate the time scale in which the the stick-slips happen leading to the bifurcations. This is fundamental to understanding the triboluminescence and acoustic emissions associated with the bifurcations. We establish a relationship between ...

We consider iterated maps with a reflectional symmetry. Possible bifurcations in such systems include period-doubling bifurcations (within the symmetric subspace) and symmetry-breaking bifurcations. By using a second parameter, these bifurcations can be made to coincide at a mode interaction. By reformulating the period-doubling bifurcation as a symmetry-breaking bifurcation, two bifurcation eq...

Abstract This paper proposes a virtual oscillator control method by reducing the order of amplitude term Andronov-Hopf dynamic process. The proposed retains its steady-state droop characteristic and power dispatchability in grid-connected mode, but with less nonlinearity. At same time, based on performance criterion inverter, detailed parameter selection principle controller is given, verified ...