References and models cited by this paper | References and models that cite this paper | |||||||
Bergman H, Wichmann T, Karmon B, DeLong MR (1994) The primate subthalamic nucleus. II. Neuronal activity in the MPTP model of parkinsonism. J Neurophysiol 72:507-20 [Journal] [PubMed] Bevan MD, Magill PJ, Terman D, Bolam JP, Wilson CJ (2002) Move to the rhythm: oscillations in the subthalamic nucleus-external globus pallidus network. Trends Neurosci 25:525-31 [PubMed] Cragg SJ, Baufreton J, Xue Y, Bolam JP, Bevan MD (2004) Synaptic release of dopamine in the subthalamic nucleus. Eur J Neurosci 20:1788-802 [Journal] [PubMed] Ermentrout GB (2002) Simulating, Analyzing, and Animating Dynamical System: A Guide to XPPAUT for Researchers and Students Society for Industrial and Applied Mathematics (SIAM) Golomb D, Rinzel J (1994) Clustering in globally coupled inhibitory neurons Physica D 72:259-282 Golomb D, Wang XJ, Rinzel J (1994) Synchronization properties of spindle oscillations in a thalamic reticular nucleus model. J Neurophysiol 72:1109-26 [Journal] [PubMed] HODGKIN AL, HUXLEY AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-44 [Journal] [PubMed] Hurtado JM, Gray CM, Tamas LB, Sigvardt KA (1999) Dynamics of tremor-related oscillations in the human globus pallidus: a single case study. Proc Natl Acad Sci U S A 96:1674-9 [PubMed] Jolliffe IT (1986) Principal component analysis Kopell N, Ermentrout GB (2002) Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators Handbook of dynamical systems, Fiedler B, ed, ed. pp.5 Kuramoto Y (1984) Chemical oscillations, waves, and turbulence Magnin M, Morel A, Jeanmonod D (2000) Single-unit analysis of the pallidum, thalamus and subthalamic nucleus in parkinsonian patients. Neuroscience 96:549-64 [PubMed] Nejshtadt A (1985) Asymptotic investigation of the loss of stability by an equilibrium as a pair of eigenvalues slowly cross the imaginary axis Uspehi Matematieskih Nauk 40:190-191 Parra P, Gulyás AI, Miles R (1998) How many subtypes of inhibitory cells in the hippocampus? Neuron 20:983-93 [PubMed] Pinkus A (2000) Weierstrass and approximation theory J Approximation Theo 107:1-66 Pinsky PF, Rinzel J (1995) Synchrony measures for biological neural networks. Biol Cybern 73:129-37 [PubMed] Raz A, Vaadia E, Bergman H (2000) Firing patterns and correlations of spontaneous discharge of pallidal neurons in the normal and the tremulous 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine vervet model of parkinsonism. J Neurosci 20:8559-71 [PubMed] Reyes AD (2003) Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro. Nat Neurosci 6:593-9 [Journal] [PubMed] Rinzel J (1985) Bursting oscillations in an excitable membrane model, in ordinary and partial differential equations New Lecture Notes in Mathematics 1151:304-316 Rinzel JA (1987) A formal classification of bursting mechanisms in excitable systems Proc Intl Congress Mathematicians, Gleason AM, ed. pp.1578 Rubin J, Terman D (2000) Geometric singular perturbation analysis of neuronal dynamics Handbook of Dynamical Systems: Towards Applications Rubin J, Terman D (2000) Geometric analysis of population rhythms in synaptically coupled neuronal networks. Neural Comput 12:597-645 [PubMed] Rubin J, Terman D (2000) Analysis of clustered firing patterns in synaptically coupled networks of oscillators. J Math Biol 41:513-45 [PubMed] Steriade M, McCormick DA, Sejnowski TJ (1993) Thalamocortical oscillations in the sleeping and aroused brain. Science 262:679-85 [PubMed] Strogatz SH, Mirollo RE (1991) Stability of incoherence in a population of coupled oscillators J Stat Phys 63:613-635 Su JZ, Rubin J, Terman D (2004) Effects of noise on elliptic bursters Nonlinearity 17:133-157 Terman D, Bose A, Kopell N (1996) Functional reorganization in thalamocortical networks: transition between spindling and delta sleep rhythms. Proc Natl Acad Sci U S A 93:15417-22 [PubMed] Terman D, Rubin JE, Yew AC, Wilson CJ (2002) Activity patterns in a model for the subthalamopallidal network of the basal ganglia. J Neurosci 22:2963-76 [Journal] [PubMed] Thunberg H (2001) Periodicity versus chaos in one-dimensional dynamics SIAM Rev 43:3-30 van Vreeswijk C, Sompolinsky H (1998) Chaotic balanced state in a model of cortical circuits. Neural Comput 10:1321-71 [PubMed] Wang XJ, Golomb D, Rinzel J (1995) Emergent spindle oscillations and intermittent burst firing in a thalamic model: specific neuronal mechanisms. Proc Natl Acad Sci U S A 92:5577-81 [PubMed] Wang XJ, Rinzel J (1992) Alternating and synchronous rhythms in reciprocally inhibitory model neurons Neural Comput 4:84-97 Wang XJ, Rinzel J (1993) Spindle rhythmicity in the reticularis thalami nucleus: synchronization among mutually inhibitory neurons. Neuroscience 53:899-904 [PubMed] Wilson CJ (2004) The basal ganglia The Synaptic Organization of the Brain, Shepherd GM, ed. pp.361 | Dovzhenok A, Park C, Worth RM, Rubchinsky LL (2013) Failure of delayed feedback deep brain stimulation for intermittent pathological synchronization in Parkinson's disease. PLoS One 8:e58264 [Journal] [PubMed]
Edgerton JR, Jaeger D (2011) Dendritic sodium channels promote active decorrelation and reduce phase locking to parkinsonian input oscillations in model globus pallidus neurons. J Neurosci 31:10919-36 [Journal] [PubMed]
Mulcahy G, Atwood B, Kuznetsov A (2020) Basal ganglia role in learning rewarded actions and executing previously learned choices: Healthy and diseased states. PLoS One 15:e0228081 [Journal] [PubMed]
|