Related Experiment Video
Updated: Jun 26, 2026

Using Insect Electroantennogram Sensors on Autonomous Robots for Olfactory Searches
Published on: August 4, 2014
On periodic solutions of neural networks via differential inclusions
1Department of Mathematics, Southeast University, Nanjing 210096, China.
Abstract:
Discontinuous dynamical systems, especially neural networks with discontinuous activation functions, arise in a number of applications and have received considerable research attention in recent years. However, there still remain some fundamental issues to be investigated, for instance, how to define the solutions of such discontinuous systems and what conditions can guarantee the existence and stability of the solutions. In this paper, based on the concept of Filippov solution, the dynamics of a general class of neural networks with discontinuous activation functions is investigated. Sufficient conditions are obtained to ensure the existence and stability of the unique periodic solution for the neural networks by using the differential inclusions theory, the Lyapunov-Krasovskii functional method and linear matrix inequality (LMI) technique. Two numerical examples are given to illustrate the theoretical results.
Related Concept Videos
Separable Differential Equations
Partial Differential Equations
Modeling with Differential Equations
Differential Equations: Problem Solving
Classification of Systems-II
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.