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A Proposal for an Application of a Max-Type Difference Equation to Epilepsy

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Differential and Difference Equations with Applications (ICDDEA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 230))

Abstract

We propose, for the sake of dialogue, that the nonautomomous reciprocal max-type difference equation,

$$\begin{aligned} x_{n+1}=\max \left\{ \frac{A_{n}^{(0)}}{x_{n}}, \frac{A_{n}^{(1)}}{x_{n-1}}, \ldots , \frac{A_{n}^{(k)}}{x_{n-k}}\right\} , \ \ n=0, 1, \ldots , \end{aligned}$$

where the parameters are positive periodic sequences and the initial conditions are positive, when \(k=1\) may serve as a phenomenological model of seizure activity as occurs in mesial (or middle) temporal lobe epilepsy.

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Correspondence to Candace M. Kent .

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Chan, D.M., Kent, C.M., Kocić, V., Stević, S. (2018). A Proposal for an Application of a Max-Type Difference Equation to Epilepsy. In: Pinelas, S., Caraballo, T., Kloeden, P., Graef, J. (eds) Differential and Difference Equations with Applications. ICDDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 230. Springer, Cham. https://doi.org/10.1007/978-3-319-75647-9_16

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