The Painlevé property, integrability and chaotic behaviour of a two-coupled Duffing oscillators

S Rajasekar; S Paul Raj

doi:10.1007/bf02847763

Nonlinear dynamics of a shell encapsulated microbubble near solid boundary in an ultrasonic field

JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES ◽

10.15282/jmes.14.3.2020.23.0568 ◽

2020 ◽

Vol 14 (3) ◽

pp. 7235-7243

Author(s):

N.M. Ali ◽

F. Dzaharudin ◽

E.A. Alias

Keyword(s):

Oscillation Amplitude ◽

Ultrasonic Field ◽

Dynamical Behaviour ◽

Ultrasound Contrast Agents ◽

Chaotic Behaviour ◽

Solid Boundary ◽

Driving Frequency ◽

Pressure Amplitude ◽

Radial Expansion ◽

Therapeutic Delivery

Microbubbles have the potential to be used for diagnostic imaging and therapeutic delivery. However, the transition from microbubbles currently being used as ultrasound contrast agents to achieve its’ potentials in the biomedical field requires more in depth understanding. Of particular importance is the influence of microbubble encapsulation of a microbubble near a vessel wall on the dynamical behaviour as it stabilizes the bubble. However, many bubble studies do not consider shell encapsulation in their studies. In this work, the dynamics of an encapsulated microbubble near a boundary was studied by numerically solving the governing equations for microbubble oscillation. In order to elucidate the effects of a boundary to the non-linear microbubble oscillation the separation distances between microbubble will be varied along with the acoustic driving. The complex nonlinear vibration response was studied in terms of bifurcation diagrams and the maximum radial expansion. It was found that the increase in distance between the boundary and the encapsulated bubble will increase the oscillation amplitude. When the value of pressure amplitude increased the single bubble is more likely to exhibit the chaotic behaviour and maximum radius also increase as the inter wall-bubble distance is gradually increased. While, with higher driving frequency the maximum radial expansion decreases and suppress the chaotic behaviour.

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Non-Linearity and Chaotic Behaviour in Cyprus Stock Market

International Journal of Financial Management ◽

10.21863/ijfm/2015.5.4.018 ◽

2015 ◽

Vol 5 (4) ◽

Author(s):

Athina Bougioukou

Keyword(s):

Lyapunov Exponent ◽

Stock Market ◽

Chaos Theory ◽

Linear Dependence ◽

Chaotic Behavior ◽

Efficient Market Hypothesis ◽

Chaotic Behaviour ◽

Maximum Lyapunov Exponent ◽

Efficient Market ◽

General Index

The intention of this research is to investigate the aspect of non-linearity and chaotic behavior of the Cyprus stock market. For this purpose, we use non-linearity and chaos theory. We perform BDS, Hinich-Bispectral tests and compute Lyapunov exponent of the Cyprus General index. The results show that existence of non-linear dependence and chaotic features as the maximum Lyapunov exponent was found to be positive. This study is important because chaos and efficient market hypothesis are mutually exclusive aspects. The efficient market hypothesis which requires returns to be independent and identically distributed (i.i.d.) cannot be accepted.

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Complexity of a Peroxidase-Oxidase Reaction Model

Physical Chemistry Chemical Physics ◽

10.1039/d0cp06153k ◽

2021 ◽

Author(s):

Jason Gallas ◽

Marcus Hauser ◽

Lars Folke Olsen

Keyword(s):

Chemical Reaction ◽

Mixed Mode ◽

Period Doubling ◽

Reaction Model ◽

Chaotic Behaviour ◽

Mixed Mode Oscillations ◽

Oscillating Reaction ◽

Oxidase Reaction

The peroxidase-oxidase oscillating reaction was the first (bio)chemical reaction to show chaotic behaviour. The reaction is rich in bifurcation scenarios, from period-doubling to peak-adding mixed mode oscillations. Here, we study...

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Symmetry-breaking bifurcations in resonant surface waves

Journal of Fluid Mechanics ◽

10.1017/s0022112089000455 ◽

1989 ◽

Vol 199 ◽

pp. 495-518 ◽

Cited By ~ 82

Author(s):

Z. C. Feng ◽

P. R. Sethna

Keyword(s):

Normal Form ◽

Symmetry Breaking ◽

Surface Waves ◽

Bifurcation Analysis ◽

Internal Resonance ◽

Travelling Waves ◽

Chaotic Behaviour ◽

Derived Set ◽

Parameter Values ◽

Theoretical Results

Surface waves in a nearly square container subjected to vertical oscillations are studied. The theoretical results are based on the analysis of a derived set of normal form equations, which represent perturbations of systems with 1:1 internal resonance and with D4 symmetry. Bifurcation analysis of these equations shows that the system is capable of periodic and quasi-periodic standing as well as travelling waves. The analysis also identifies parameter values at which chaotic behaviour is to be expected. The theoretical results are verified with the aid of some experiments.

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