Hopf bifurcation mechanism analysis in an improved cortex-basal ganglia network with distributed delays: An application to Parkinson’s disease

Wang, Zhizhi; Hu, Bing; Zhou, Weiting; Xu, Minbo; Wang, Dingjiang

doi:10.1016/j.chaos.2022.113022

Cited by 10 publications

(3 citation statements)

References 99 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Indeed, distributed delays can more truly describe the delay effects of signal transmissions between different neurons. Wang et al also considered a Parkinson's model with distributed delays [5]:…”

Section: Introductionmentioning

confidence: 99%

“…where K 1 , K 2 , and K 3 represent the weak or strong gamma functions. The authors studied the stable, conditional stable, conditional oscillation, and absolute oscillation for model (5), which can explain different mechanisms of oscillation origin. Agiza et al used the Taylor series transform to discuss two-delay differential equations for the Parkinson's disease models in [6].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Oscillatory Behavior of the Solutions for a Parkinson’s Disease Model with Discrete and Distributed Delays

Feng

2024

Axioms

View full text Add to dashboard Cite

In this paper, the oscillatory behavior of the solutions for a Parkinson’s disease model with discrete and distributed delays is discussed. The distributed delay terms can be changed to new functions such that the original model is equivalent to a system in which it only has discrete delays. Using Taylor’s expansion, the system can be linearized at the equilibrium to obtain both the linearized part and the nonlinearized part. One can see that the nonlinearized part is a disturbed term of the system. Therefore, the instability of the linearized system implies the instability of the whole system. If a system is unstable for a small delay, then the instability of this system will be maintained as the delay increased. By analyzing the linearized system at the smallest delay, some sufficient conditions to guarantee the existence of oscillatory solutions for a delayed Parkinson’s disease system can be obtained. It is found that under suitable conditions on the parameters, time delay affects the stability of the system. The present method does not need to consider a bifurcating equation. Some numerical simulations are provided to illustrate the theoretical result.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Oscillatory Behavior of the Solutions for a Parkinson’s Disease Model with Discrete and Distributed Delays

Feng

2024

Axioms

View full text Add to dashboard Cite

show abstract

“…Many authors have investigated the nonlinear dynamics in Parkinson's disease by means of the experimental method or analytical method . For example, Wang et al described the model by mean-field firing rate equations with discrete and distributed delays [12]:…”

Section: Introductionmentioning

confidence: 99%

Periodic Oscillation of the Solutions for a Parkinson's Disease Model

Feng

2023

ARJOM

View full text Add to dashboard Cite

In this paper, the oscillation of the solutions for a Parkinson's disease model with multiple delays is discussed. By linearizing the system at the equilibrium point and analyzing the instability of the linearized system, some sufficient conditions to guarantee the existence of periodic oscillation of the solutions for a delayed Parkinson's disease system are obtained. It is found that under suitable conditions on the parameters, time delay affects the stability of the system. The present method does not need to consider a bifurcating equation. Some numerical simulations are provided to illustrate our theoretical prediction.

show abstract

Controlling Alzheimer’s disease by deep brain stimulation based on a data-driven cortical network model

Yan,

Yang,

Duan

2024

Cogn Neurodyn

View full text Add to dashboard Cite

Hopf bifurcation mechanism analysis in an improved cortex-basal ganglia network with distributed delays: An application to Parkinson’s disease

Cited by 10 publications

References 99 publications

Oscillatory Behavior of the Solutions for a Parkinson’s Disease Model with Discrete and Distributed Delays

Oscillatory Behavior of the Solutions for a Parkinson’s Disease Model with Discrete and Distributed Delays

Periodic Oscillation of the Solutions for a Parkinson's Disease Model

Controlling Alzheimer’s disease by deep brain stimulation based on a data-driven cortical network model

Contact Info

Product

Resources

About