Learn More
A fundamental step in synthetic biology and systems biology is to derive appropriate mathematical models for the purposes of analysis and design. For example, to synthesize a gene regulatory network, the derivation of a mathematical model is important in order to carry out in silico investigations of the network dynamics and to investigate parameter(More)
In Parkinson's disease, an increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with difficulty in movement initiation. An important role in the generation of these oscillations is thought to be played by the motor cortex and by a network composed of the subthalamic nucleus (STN) and the external segment of globus(More)
We use blowup to study the regularization of codimension one two-fold singularities in planar piecewise smooth (PWS) dynamical systems. We focus on singular canards, pseudo-equlibria and limit cycles that can occur in the PWS system. Using the regularization of Sotomayor and Teixeira [30], we show rigorously how singular canards can persist and how the(More)
Users may access full items free of charge; copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational or not-for-profit purposes without prior permission or charge, provided: • The authors, title and full bibliographic details is credited in(More)
Tumour growth rates have been measured in metastatic non-seminomatous germ cell testicular tumours (NSGCTT) by estimating the rate of rise of tumour marker production (TMP). TMP was calculated for the time between orchidectomy and the start of chemotherapy in a group of 58 patients with metastatic NSGCTT treated with BEP combination chemotherapy (bleomycin,(More)
A key pathology in the development of Parkinson's disease is the occurrence of persistent beta oscillations, which are correlated with difficulty in movement initiation. We investigated the network model composed of the subthalamic nucleus (STN) and globus pallidus (GP) developed by A. Nevado Holgado et al. [(2010) Journal of Neuroscience, 30, 12340-12352],(More)
In this paper we describe a method for continuing periodic solution bifurcations in periodic delay-differential equations. First, the notion of characteristic matrices of periodic orbits is introduced and equivalence with the monodromy operator is proved. An alternative formulation of the characteristic matrix is given, which can efficiently be computed.(More)