Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential...

Area of Science:

• Dynamical Systems Modeling
• Longitudinal Data Analysis
• Homeostatic Systems

Background:

• Self-regulated homeostatic systems are crucial in physiology and social sciences.
• Analyzing longitudinal data from these systems, especially during excitations, presents challenges.
• Existing methods may not fully capture the dynamic response to external stimuli.

Purpose of the Study:

• To propose a dynamical system modeling approach for analyzing longitudinal data of homeostatic systems.
• To model the evolution of physiological signals before, during, and after excitations.
• To extract simple, characteristic parameters describing system behavior and response.

Main Methods:

• Development of a first-order linear differential equation model with constant coefficients.
• Inclusion of three key parameters: initial equilibrium, dynamic characteristic time, and reaction to excitation.
• A two-step estimation procedure accounting for interindividual variability (random effects).

Main Results:

• The proposed model successfully characterizes signal evolution during and after excitations.
• A simulation study validated the accuracy of parameter estimation under various conditions.
• The model demonstrated practical applicability with cardiology data from effort tests.

Conclusions:

• The dynamical system modeling approach provides a robust method for analyzing homeostatic system responses.
• The extracted parameters offer simple yet informative characteristics of physiological and psychosocial processes.
• This approach is broadly applicable across medicine and social sciences for understanding system dynamics.