A generic mechanism for spatiotemporal intermittency

Argentina, Médéric; Coullet, P.

doi:10.1016/s0378-4371(98)00213-1

Cited by 15 publications

(16 citation statements)

References 22 publications

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“…changes in the equilibrium point structure of the underlying equations, which due to reflection symmetry are of pitchfork type. Furthermore interplay between stationary and dynamic bifurcations may lead to more complicated dynamics such as spatio-temporal intermittency and chaos (Argentina and Coullet, 1998 …”

Section: Introductionmentioning

confidence: 99%

Bifurcations in nonlinear models of fluid-conveying pipes supported at both ends

Nikolić

Rajković

2006

Journal of Fluids and Structures

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Stationary bifurcations in several nonlinear models of fluid conveying pipes fixed at both ends are analyzed with the use of Lyapunov-Schmidt reduction and singularity theory. Influence of the gravitational force, curvature and vertical elastic support on various properties of bifurcating solutions are investigated. In particular the conditions for occurrence of supercritical and subcritical bifurcations are presented for the models of Holmes, Thurman and Mote, and Paidoussis. r

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Section: Introductionmentioning

confidence: 99%

Bifurcations in nonlinear models of fluid-conveying pipes supported at both ends

Nikolić

Rajković

2006

Journal of Fluids and Structures

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“…Modeling results also identify and describe a fairly broad domain of existence of spatio-temporal chaos. The phenomenon of spatio-temporal chaos is gaining increasing attention in recent time, and it has been studied by many authors [14][15][16][17]. A detailed review of the complex chaotic behavior observable in physical and chemical systems is provided in [14].…”

Section: Introductionmentioning

confidence: 99%

“…A detailed review of the complex chaotic behavior observable in physical and chemical systems is provided in [14]. A characteristic mechanism of transition to chaos is described in [15]. Several models of spatio-temporal chaos are also described in [15].…”

Section: Introductionmentioning

confidence: 99%

“…A characteristic mechanism of transition to chaos is described in [15]. Several models of spatio-temporal chaos are also described in [15]. In [16], the complex chaotic behavior is investigated by the method of empirical orthogonal functions or the orthogonal decomposition method (Karhunen-Loeve decomposition), which provides a powerful tool for the analysis of complex spatio-temporal structures in reactions on the surface of a catalyst.…”

Section: Introductionmentioning

confidence: 99%

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Natural waves and chaotic structures in a distributed four-component model of the NO+CO/PT(100) reaction

Kurkina¹,

Malykh²,

Makeev³

1999

Comput Math Model

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The paper investigates the spatio-temporal structures arising in the distributed model of the NO + CO/Pt(100) reaction. Different types of spatio-temporal structures are identified. Their existence domains are plotted on a bifurcation diagram in the (T, P) parameter plane for a fixed pressure P. Spatio-temporal structures are investigated in excitable and bistable media, such as single traveling pulses and switching waves. Spatio-temporal chaos is shown to exist in a fairly wide range. The system is highly sensitive to initial conditions, which confirms its complex chaotic behavior. It is shown that the new reaction-diffusion model describes the basic features of experimental observations. This model also predicts some interesting phenomena, such as formation of localized pulses (both stationary and breathing), that so far have not been observed experimentally.

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“…This bifurcation is general for the occurrence of spatiotemporal intermittency, as seen in several different systems. 9 We first study the Gray-Scott model with differential diffusivities. The model reads…”

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confidence: 99%