Research output per year
Research output per year
L. Spek, K. Dijkstra, S.A. van Gils, M. Polner
Research output: Contribution to journal › Article › Academic › peer-review
Delayed neural field models can be viewed as a dynamical system in an appropriate functional analytic setting. On two dimensional rectangular space domains, and for a special class of connectivity and delay functions, we describe the spectral properties of the linearized equation. We transform the characteristic integral equation for the delay differential equation (DDE) into a linear partial differential equation (PDE) with boundary conditions. We demonstrate that finding eigenvalues and eigenvectors of the DDE is equivalent with obtaining nontrivial solutions of this boundary value problem (BVP). When the connectivity kernel consists of a single exponential, we construct a basis of the solutions of this BVP that forms a complete set in L 2. This gives a complete characterization of the spectrum and is used to construct a solution to the resolvent problem. As an application we give an example of a Hopf bifurcation and compute the first Lyapunov coefficient.
Original language | English |
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Pages (from-to) | 439-473 |
Number of pages | 35 |
Journal | Journal of differential equations |
Volume | 317 |
Early online date | 15 Feb 2022 |
DOIs | |
Publication status | Published - 25 Apr 2022 |
Research output: Thesis › PhD Thesis - Research UT, graduation UT
Research output: Working paper › Preprint › Academic