Parkinson J (2002) An essay on the shaking palsy. The Journal of neuropsychiatry and clinical neurosciences 14(2):223–236

Article  PubMed  Google Scholar 

Aarsland D, Batzu L, Halliday GM, Geurtsen GJ, Ballard C, Ray Chaudhuri K, Weintraub D (2021) Parkinson disease-associated cognitive impairment. Nature Reviews Disease Primers 7(1):47

Article  PubMed  Google Scholar 

Jankovic J (2008) Parkinson’s disease: clinical features and diagnosis. Journal of neurology, neurosurgery & psychiatry 79(4):368–376

Article  CAS  Google Scholar 

Leventhal DK, Gage GJ, Schmidt R, Pettibone JR, Case AC, Berke JD (2012) Basal ganglia beta oscillations accompany cue utilization. Neuron 73(3):523–536

Article  CAS  PubMed  PubMed Central  Google Scholar 

McGregor MM, Nelson AB (2019) Circuit mechanisms of parkinson’s disease. Neuron 101(6):1042–1056

Article  CAS  PubMed  Google Scholar 

Holt AB, Netoff TI (2014) Origins and suppression of oscillations in a computational model of parkinson’s disease. Journal of computational neuroscience 37:505–521

Article  MathSciNet  PubMed  PubMed Central  Google Scholar 

Hu B, Wang Z, Xu M, Zhang D, Wang D (2022) The adjustment mechanism of the spike and wave discharges in thalamic neurons: a simulation analysis. Cognitive Neurodynamics 16(6):1449–1460

Article  PubMed  PubMed Central  Google Scholar 

Muddapu VR, Chakravarthy VS (2020) A multi-scale computational model of excitotoxic loss of dopaminergic cells in parkinson’s disease. Frontiers in Neuroinformatics 14:34

Article  PubMed  PubMed Central  Google Scholar 

Shouno O, Tachibana Y, Nambu A, Doya K (2017) Computational model of recurrent subthalamo-pallidal circuit for generation of parkinsonian oscillations. Frontiers in neuroanatomy 11:21

Article  PubMed  PubMed Central  Google Scholar 

Muddapu VR, Mandali A, Chakravarthy VS, Ramaswamy S (2019) A computational model of loss of dopaminergic cells in parkinson’s disease due to glutamate-induced excitotoxicity. Frontiers in neural circuits 13:11

Article  CAS  PubMed  PubMed Central  Google Scholar 

Holgado AJN, Terry JR, Bogacz R (2010) Conditions for the generation of beta oscillations in the subthalamic nucleus-globus pallidus network. Journal of Neuroscience 30(37):12340–12352

Article  CAS  PubMed  Google Scholar 

Pavlides A, John Hogan S, Bogacz R (2012) Improved conditions for the generation of beta oscillations in the subthalamic nucleus-globus pallidus network. European Journal of Neuroscience 36(2):2229–2239

Article  PubMed  Google Scholar 

Bevan MD, Atherton JF, Baufreton J (2006) Cellular principles underlying normal and pathological activity in the subthalamic nucleus. Current opinion in neurobiology 16(6):621–628

Article  CAS  PubMed  Google Scholar 

Tachibana Y, Iwamuro H, Kita H, Takada M, Nambu A (2011) Subthalamo-pallidal interactions underlying parkinsonian neuronal oscillations in the primate basal ganglia. European Journal of Neuroscience 34(9):1470–1484

Article  PubMed  Google Scholar 

Nevado-Holgado AJ, Terry JR, Bogacz R (2011) Bifurcation analysis points towards the source of beta neuronal oscillations in parkinson’s disease. In: 2011 50th IEEE Conference on Decision and Control and European Control Conference, pp. 6492–6497. IEEE

Chen M, Zhu Y, Zhang R, Yu R, Hu Y, Wan H, Yao D, Guo D (2023) A model description of beta oscillations in the external globus pallidus. Cognitive Neurodynamics 17(2):477–487

Article  PubMed  Google Scholar 

Chen Y, Wang J, Kang Y, Ghori MB et al (2020) Emergence of beta oscillations of a resonance model for parkinson’s disease. Neural plasticity 2020

Wang Z, Hu B, Zhu L, Lin J, Xu M, Wang D (2022) Hopf bifurcation analysis for parkinson oscillation with heterogeneous delays: A theoretical derivation and simulation analysis. Communications in Nonlinear Science and Numerical Simulation 114:106614

Article  MathSciNet  Google Scholar 

Rahman B, Kyrychko Y, Blyuss K, Hogan S (2018) Dynamics of a subthalamic nucleus-globus palidus network with three delays. IFAC-PapersOnLine 51(14):294–299

Article  Google Scholar 

Pavlides A, Hogan SJ, Bogacz R (2015) Computational models describing possible mechanisms for generation of excessive beta oscillations in parkinson’s disease. PLoS computational biology 11(12):1004609

Article  ADS  Google Scholar 

Wang Z, Hu B, Zhu L, Lin J, Xu M, Wang D (2023) The possible mechanism of direct feedback projections from basal ganglia to cortex in beta oscillations of parkinson’s disease: A theoretical evidence in the competing resonance model. Communications in Nonlinear Science and Numerical Simulation 120:107142

Article  MathSciNet  Google Scholar 

Yan H, Wang J (2017) Quantification of motor network dynamics in parkinson’s disease by means of landscape and flux theory. PloS one 12(3):0174364

Article  Google Scholar 

Eugeni M, Dessi D, Mastroddi F (2018) A normal form analysis in a finite neighborhood of a hopf bifurcation: on the center manifold dimension. Nonlinear Dynamics 91:1461–1472

Article  Google Scholar 

Ruan S, Wei J (2003) On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynamics of Continuous Discrete and Impulsive Systems Series A 10:863–874

MathSciNet  Google Scholar 

DeJesus EX, Kaufman C (1987) Routh-hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations. Physical Review A 35(12):5288

Article  ADS  MathSciNet  CAS  Google Scholar 

Yi G, Wang L, Chu C, Liu C, Zhu X, Shen X, Li Z, Wang F, Yang M, Wang J (2022) Analysis of complexity and dynamic functional connectivity based on resting-state eeg in early parkinson’s disease patients with mild cognitive impairment. Cognitive Neurodynamics, 1–15

Yu Y, Han F, Wang Q, Wang Q (2021) Model-based optogenetic stimulation to regulate beta oscillations in parkinsonian neural networks. Cognitive Neurodynamics, 1–15

Xu M, Hu B, Wang Z, Zhu L, Lin J, Wang D (2023) Mathematical derivation and mechanism analysis of beta oscillations in a cortex-pallidum model. Cognitive Neurodynamics, 1–20

Huang C, Mo S, Cao J (2023) Detections of bifurcation in a fractional-order cohen-grossberg neural network with multiple delays. Cognitive Neurodynamics, 1–18

Zhao L, Huang C, Cao J (2022) Effects of double delays on bifurcation for a fractional-order neural network. Cognitive Neurodynamics, 1–13

Bönsel F, Krauss P, Metzner C, Yamakou ME (2022) Control of noise-induced coherent oscillations in three-neuron motifs. Cognitive Neurodynamics 16(4):941–960

Article  PubMed  Google Scholar