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Road to chaos in a Duflng oscillator with time delay loop

Borkowski Łukasz

Mechanics and Mechanical Engineering

2021

Vol. 25, nr 1

84--87

This article examines a single Duffing oscillator with a time delay loop. The research aims to check the impact of the time delay value on the nature of the solution, in particular the scenario of transition to a chaotic solution. Dynamic tools such as bifurcation diagrams, phase portraits, Poincaré maps, and FFT analysis will be used to evaluate the obtained results.

Determination of Hopf bifurcation sets of a chemicalreactors by two-parameter continuation method

Berezowski Marek

Chemical and Process Engineering

2020

Vol. 41, nr 3

221-–227

A two-parameter continuation method was developed and shown in the form of an example, allowingdetermination of Hopf bifurcation sets in a chemical reactor model. Exemplary calculations weremade for the continuous stirred tank reactor model (CSTR). The set of HB points limiting the rangeof oscillation in the reactor was determined. The results were confirmed on the bifurcation diagramof steady states and on time charts. The method is universal and can be used for various models ofchemical reactors.

Dynamice of three unidirectionally coupled Duffing oscillators

Borkowski Ł.

Mechanics and Mechanical Engineering

2011

Vol. 15, nr 2

125-132

This article presents a system of three unidirectionally coupled Duffing oscillators. On the basic of numerical study we show the mechanism of translation from steady state to chaotic and hyperchaotic behavior. Additionally, the impact of parameter changes on the behavior of the system will be presented. Confirmation of our results are bifurcation diagrams, timelines, phase portraits, Poincare maps and largest Lyapunov exponent diagrams.

Bifurcation diagram for drive system

Houfek L., Kratochvil C., Krejsa J., Navrat T

Modelling and Optimization of Physical Systems

2008

z. 7

43--46

The paper is focused on analysis of dynamic properties of drive systems. It describes the possible ways of stability analysis and possible ways of analysis of bifurcation of steady states and possible occurrence of chaotic behavior.