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Global Bifurcation

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Non-Local Cell Adhesion Models

Part of the book series: CMS/CAIMS Books in Mathematics ((CMS/CAIMS BM,volume 1))

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Abstract

For each \(\bar {u}>0\), we found local bifurcations at \((\alpha _n, \bar {u})\) with non-trivial eigenfunctions e n of \({\mathcal {D}}_u {\mathcal {F}}(\alpha _n, \bar {u})\) in \(H^2_P\) be given by

$$\displaystyle \alpha _n = \frac {n \pi }{\bar {u} h'(\bar {u}) L M_n(\omega )} , \qquad e_n(x) = \cos \left (\frac {2 \pi n x}{L}\right ), $$

where M n(ω) are the Fourier sine coefficients of ω (see 3.4).

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Notes

  1. 1.

    www.buttenschoen.ca.

  2. 2.

    http://www.mathematik.uni-halle.de/wissenschaftliches_rechnen/forschung/software/.

  3. 3.

    https://docs.scipy.org/doc/numpy-dev/f2py/.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, BC, Canada

    Andreas Buttenschön

  2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada

    Thomas Hillen

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Buttenschön, A., Hillen, T. (2021). Global Bifurcation . In: Non-Local Cell Adhesion Models. CMS/CAIMS Books in Mathematics, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-030-67111-2_5

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