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Finger Dynamics in Pattern Forming Systems

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Nonlinear Dynamics: Materials, Theory and Experiments

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 173))

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Abstract

Macroscopic systems subjected to external forcing exhibit complex spatiotemporal behaviors as result of dissipative self-organization. We consider a paradigmatic Swift-Hohenberg equation in both variational and nonvariational forms in two-dimensions. We investigate in both equations the occurrence of a curvature instability generating spot multiplication, self-replication or fingering instability that affects the circular shape of two-dimensional localized structures . We show that when increasing the radius of localized structures, the first angular index m to become unstable is \(m=2\). This mode corresponds to an elliptical deformation of the circular shape of localized structures. We show also that for a fixed value of the radius of localized structures, the mode \(m=2\) becomes unstable for small values of the diffusion coefficient and higher modes become unstable for large angular index m. These result hold for both variational and nonvariational models. In addition, we analyze the stability of a single stripe localized structure and extended pattern for both variational and nonvariational Swift-Hohenberg equations.

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Acknowledgments

M.G.C. thanks the financial support of FONDECYT project 1120320. I.B. is supported by CONICYT, Beca de Magister Nacional.

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Authors and Affiliations

  1. Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile

    Ignacio Bordeu

  2. Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile

    Marcel G. Clerc

  3. Faculté des Sciences, Université Libre de Bruxelles (U.L.B.), CP 231, Campus Plaine, 1050, Bruxelles, Belgium

    René Lefever & Mustapha Tlidi

Authors
  1. Ignacio Bordeu
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  2. Marcel G. Clerc
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  3. René Lefever
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  4. Mustapha Tlidi
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Corresponding author

Correspondence to Ignacio Bordeu .

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Editors and Affiliations

  1. Physique des systèmes dynamiques, Université Libre de Bruxelles, Brussels, Belgium

    Mustapha Tlidi

  2. Universidad de Chile, Santiago, Chile

    Marcel. G. Clerc

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Bordeu, I., Clerc, M.G., Lefever, R., Tlidi, M. (2016). Finger Dynamics in Pattern Forming Systems. In: Tlidi, M., Clerc, M. (eds) Nonlinear Dynamics: Materials, Theory and Experiments. Springer Proceedings in Physics, vol 173. Springer, Cham. https://doi.org/10.1007/978-3-319-24871-4_21

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