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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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Related Experiment Video

Updated: Jun 26, 2026

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

Multistability and arithmetically period-adding bifurcations in piecewise smooth dynamical systems.

Younghae Do¹, Ying-Cheng Lai

¹Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea.

Chaos (Woodbury, N.Y.)

|January 7, 2009

Summary

Researchers explored multistability in nonsmooth dynamical systems, finding that periodic attractors emerge with periods in an arithmetic sequence near the Hamiltonian limit. This phenomenon is unique to nonsmooth systems.

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Last Updated: Jun 26, 2026

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

Area of Science:

Nonlinear Dynamics
Nonsmooth Dynamical Systems
Bifurcation Theory

Background:

Multistability is a key phenomenon in nonlinear dynamics, with most research focused on smooth systems.
Nonsmooth dynamical systems are prevalent in real-world applications like impact oscillators and electronic circuits.

Purpose of the Study:

To investigate multistability in piecewise smooth dynamical systems.
To analyze the behavior of these systems in the weakly dissipative regime and the Hamiltonian limit.

Main Methods:

Consideration of a generic class of piecewise smooth dynamical systems in normal form.
Analysis focused on the weakly dissipative regime and the approach to the Hamiltonian limit.
Utilized physical analyses, numerical computations, and rigorous mathematical arguments.

Main Results:

Periodic attractors are generated through saddle-node bifurcations as the Hamiltonian limit is approached.
A novel phenomenon observed: the periods of newly generated attractors follow an arithmetic sequence.
This arithmetic progression of periods is not observed in smooth dynamical systems.

Conclusions:

Nonsmooth dynamical systems exhibit unique multistability phenomena not seen in smooth systems.
The generation of periodic attractors with arithmetic sequence periods is a significant finding.
The study provides a theoretical and computational basis for understanding multistability in complex systems.