Comparison of some experimental data and deterministic dynamical models of heartbeat show that it is essential to consider stochastic mathematical models. The Zeeman heartbeat model is one of the main heartbeat models whose stochastic dynamics is less studied. Especially, investigating bifurcations in stochastic dynamical models can be useful for identifying abnormal cardiac rhythms. This paper is concerned with two essential features of the two dimensional stochastic Zeeman heartbeat model i.e., stability and bifurcation. To achieve this approach, Taylor expansion, polar coordinate transformation, and stochastic averaging procedure will be used to convert the classical system into an Ito averaging diffusion system. Furthermore, we consider several theorems which provide sufficient conditions of drift and diffusion coefficients to establish stochastic stability, D-bifurcation and phenomenological bifurcation of the model. In the end, numerical simulation plays an important role to show the influences of the noise severity and confirm our theoretical results.
Download full-text PDF |
Source |
|---|
Publication Analysis
Top Keywords
Similar Publications
Stability and Bifurcation in the Two-Dimensional Stochastic Zeeman Heartbeat Model.
Nonlinear Dynamics Psychol Life Sci
April 2023
Yazd University, Yazd, Iran.
Comparison of some experimental data and deterministic dynamical models of heartbeat show that it is essential to consider stochastic mathematical models. The Zeeman heartbeat model is one of the main heartbeat models whose stochastic dynamics is less studied. Especially, investigating bifurcations in stochastic dynamical models can be useful for identifying abnormal cardiac rhythms.
View Article and Find Full Text PDFCatastrophe theory in work from heartbeats to eye movements.
Biol Cybern
February 2021
University of Toronto, Toronto, ON, USA.
In "Slow-fast control of eye movements: an instance of Zeeman's model for an action," Clement and Akman extended Zeeman's model for the heartbeat to describe eye movement control of different species using aspects of catastrophe theory. The scientists created a model that gives an example of how the techniques of catastrophe theory can be used to understand information processing by biological organisms, a key aspect of biological cybernetics. They tested how well the system of equations for Zeeman's model could be applied to saccadic eye movements.
View Article and Find Full Text PDFIs altered behavior linked to cellular energy regulation in a freshwater mussel (Elliptio complanata) exposed to triclosan?
Comp Biochem Physiol C Toxicol Pharmacol
January 2016
Department of Marine Sciences, University of New England, 11 Hills Beach Rd., Biddeford, ME 04005, USA. Electronic address:
Environmental stress may alter the bioenergetic balance of organisms by resulting in greater energy investment into detoxification processes, which diverts energy from other biological functions. Here, we examine responses to triclosan (TCS) exposure in a freshwater mussel across multiple biological levels: behavioral (e.g.
View Article and Find Full Text PDFNon-invasive assessment of maternal hemodynamics in early pregnancy.
Pregnancy Hypertens
October 2013
Department of Obstetrics and Gynecology, Lyell McEwin Hospital, University of Adelaide, Adelaide, South Australia, Australia. Electronic address:
Objectives: Non-invasive assessment of maternal hemodynamics in early pregnancy may be promising in evaluating maternal hemodynamic (mal)adaptation to pregnancy. We explored usage of applanation tonometry and Doppler ultrasound for assessment of cardiac output (CO), systemic vascular resistance (SVR) and arterial stiffness in early pregnancy.
Methods: Pregnant healthy nulliparous women were studied during first trimester.
Effect of intensive outpatient physical training on gait performance and cardiovascular health in people with hemiparesis after stroke.
Phys Ther
April 2010
Center for Rehabilitation of Brain Injury, University of Copenhagen, Amagerfaelledveg 56A, DK-2300 Copenhagen, Denmark.
Background: Stroke can result in severe motor deficits, and many people who have survived a stroke have poor cardiovascular fitness, with potentially disabling effects on daily life.
Objective: The objective of this study was to evaluate the impact of intensive physical training on gait performance and cardiovascular health parameters in people with stroke in the chronic stage.
Design: This was a single-group, pretest-posttest experimental study.
Want AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!