16 citations · 32 across the 8 of their papers we have counts for
5 papers · 1 filter
Numerical Periodic Normalization at Codim 1 Bifurcations of Limit Cycles in DDEs
M. M. Bosschaert, B. Lentjes, L. Spek +1
Recent work in [53, 54] by the authors on periodic center manifolds and normal forms for bifurcations of limit cycles in delay differential equations (DDEs) motivates the derivatio…
Bifurcations of Neural Fields on the Sphere
Len Spek, Stephan A. van Gils, Yuri A. Kuznetsov +1
A common model to study pattern formation in large groups of neurons is the neural field. We investigate a neural field with excitatory and inhibitory neurons, like Wilson and Cowa…
Periodic Center Manifolds for DDEs in the Light of Suns and Stars
B. Lentjes, L. Spek, M. M. Bosschaert +1
In this paper we prove the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in classical delay differential equations by using the Lyapu…
Dynamics of delayed neural field models in two-dimensional spatial domains
L. Spek, M. Polner, K. Dijkstra +1
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…
Neural Field Models with Transmission Delays and Diffusion
Len Spek, Yuri A. Kuznetsov, Stephan A. van Gils
A neural field models the large scale behaviour of large groups of neurons. We extend results of van Gils et al. [2013] and Dijkstra et al. [2015] by including a diffusion term int…