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BIBO stability of continuous and discrete -time systems

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents.

Paul L Salceanu¹

¹Mathematics Department, University of Louisiana at Lafayette, Lafayette, LA 70504, USA. salceanu@louisiana.edu

Mathematical Biosciences and Engineering : MBE

|June 17, 2011

Summary

This study introduces a unified approach for discrete and continuous dynamical systems, relaxing dissipativity assumptions. It establishes conditions for robust uniform persistence, applicable to disease dynamics in host populations.

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Area of Science:

Dynamical Systems Theory
Mathematical Biology
Nonlinear Dynamics

Background:

Previous work utilized Lyapunov exponents for uniform persistence in dissipative discrete-time systems.
Dissipativity assumptions limited the applicability of prior persistence criteria.
Understanding robust uniform persistence is crucial for ecological and epidemiological modeling.

Purpose of the Study:

To develop a unified framework for analyzing uniform persistence in both discrete and continuous time dynamical systems.
To relax the strict dissipativity assumption, broadening the scope of persistence analysis.
To establish sufficient conditions for robust uniform weak repellers and uniform persistence.

Main Methods:

Extension of Lyapunov exponent techniques to a broader class of dynamical systems.
Analysis of compact subsets of invariant parts of the boundary of the positive orthant (R(m+)).
Development of conditions based on positive Lyapunov exponents for repeller properties.

Main Results:

Sufficient conditions for robust uniform weak repellers are derived for invariant boundary sets.
Positive Lyapunov exponents on these sets are shown to be key for establishing repeller properties.
The framework successfully demonstrates robust uniform persistence, with an application to disease dynamics.

Conclusions:

The unified approach effectively extends persistence analysis to non-dissipative systems.
Lyapunov exponents provide powerful tools for characterizing robust uniform persistence.
The findings have direct implications for modeling the persistence of diseases in populations.