ISSN 0869-6632 (Online)
ISSN 2542-1905 (Print)


The role of oxygen in briggs–rauscher autooscillating reaction

It is description of the way in which chemical environment of Briggs–Rauscher autooscillating reaction a?ects characteristics of oscillations. It has been ascertained that variations of the iodide complexes concentrations perhaps occurs due to increases of oxygen concentration in media and intermediate’s concentration ?uctuation. In?uence was investigated one of the basic natural oxidizing agent oxygen and it radical forms on autocooperative mechanisms of Briggs–Rauscher reaction.

Autonomous system generating hyperbolic chaos: circuit simulation and experiment

We consider an electronic device, which represents an autonomous dynamical system with hyperbolic attractor of the Smale–Williams type in the Poincare map. Simulation ? of chaotic dynamics in the software environment Multisim has been undertaken. The generator of hyperbolic chaos is implemented as a laboratory model; its experimental investigation is carried out, and good compliance with the observed dynamics in the numerical and circuit simulation has been demonstrated.

Doubling and destruction of the tri-frequencies torus in the nonlinear oscillator under quasi-periodic exitation: experiment

In present paper nonlinear oscillator driving by external force in a form of three harmonic signals with irrational ratios of the frequencies and the map of various dynamical regimes on the parameter plane are presented. The feature of tri-frequencies torus doubling and destruction are investigated.

Bifurcations and transitions to chaos in superlattice coupled to external resonator

In this letter we study nonlinear dynamics and transition to chaos in semiconductor superlattice coupled to external linear resonator. We have shown that such system demonstrates chaotic dynamics in wide range of supply voltage, whereas in autonomous superlattice only periodical dynamics exists. Revealed that transition to chaos in system goes through intermittency.

Formation of a multi-domain spatial structure in gaas gunn diode as a nonlinear phenomenon

Experimental studies of stationary distributions of the electric ?eld intensity and the concentration of charge carriers in the Gunn diode have been provided by using near-?eld microwave microscope. The numerical computer calculation of these quantities based on the dependence of electrons mobility and di?usion coe?cient on the electric ?eld has been carried out. The existence of a multidomain mode of Gunn diodes has been found experimentally and con?rmed theoretically.

Investigation of regular and chaotic dynamics of one financial system

Based on complex numerical investigation for the nonlinear ?nancial system introduced by Chen a map of dynamic regimes has been built, depending on the bifurcation parameters. All the major scenarios of transition to deterministic chaos have been found. Theorems of the existence of the globally exponentially attractive set and positive invariant, of periodic solutions, of Poincare–Andronov–Hopf bifurcation existence and theorems in the ?eld of control of attractors are proved.

System of three non-autonomous oscillators with hyperbolic chaos chapter 2 the model with da-attractor

  We consider a system of three coupled non-autonomous van der Pol oscillators, in which the behavior of the phases over a characteridtic period is described approximately by the Fibonacci map with modi?cation of the «Smale surgery», which leads to the appearance of DA-attractor («Derived from Anosov»). According to the numerical results, the attractor of the stroboscopic map is placed approximately on a two-dimensional torus embedded in the six-dimensional phase space and has transverse Cantor-like structure typical for this kind of attractrors.

New type of bifurcations in the modified rayleigh–benard ? convection problem

The original Rayleigh–Benard convection is a standard example of the system where bifurcations occur with changing of a control parameter. In this paper we consider the modi?ed Rayleigh–Benard convection problem including radiative e?ects as well as gas sources on a surface. Such formulation leads to the identi?cation of new type of bifurcations in the problem besides the well-known Benard cells. This problem is very important for mathematics of climate because it proves the occurrence of the climate system tipping point related to greenhouse gas emission into the atmosphere.

«oscillator death» and quasiperiodic bifurcations in low- dimensional ensemble of van der pol oscillators

The dynamics of the four dissipatively coupled van der Pol oscillator is considered. Lyapunov chart is presented in the parameter plane and its arrangement is discusses. The e?ect of increase of the threshold for the «oscillator death» regime and the possibility of complete and partial broadband synchronization are revealed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators, in particular, quasi-periodic saddle-node and Hopf bifurcations.

Oscillatory media properties influence on excitation propagation

We study synchronization in ensembles of locally di?usive coupled Bonhoe?er–van der Pol oscillators. Individual elements frequencies in?uence on excitation propagation in one- and two-dimensional media is investigated. We show that excitation propagation speed depends on frequency mismatch between synchronization frequency and elements’ individual frequencies. Qualitative and quantitative results describing this e?ect are numerical modeling data and analytical research.