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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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Periodicity and stability for variable-time impulsive neural networks.

Hongfei Li1, Chuandong Li1, Tingwen Huang2

  • 1Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China.

Neural Networks : the Official Journal of the International Neural Network Society
|July 22, 2017
PubMed
Summary
This summary is machine-generated.

This study analyzes neural networks with variable-time impulses, demonstrating their reduction to fixed-time impulse models. It establishes criteria for periodic solutions and global exponential stability, confirming similar stability properties between the two models.

Keywords:
Comparison principleGlobal exponential stabilityNeural networksPeriodic solutionVariable-time impulses

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Area of Science:

  • Dynamical Systems
  • Computational Neuroscience
  • Control Theory

Background:

  • Neural networks with impulses are crucial for modeling complex biological and artificial systems.
  • Variable-time impulses introduce challenges in analyzing system dynamics and stability.
  • Existing models often rely on fixed-time impulses, limiting applicability.

Purpose of the Study:

  • To analyze a general neural network model with variable-time impulses.
  • To establish conditions for the reduction of variable-time impulsive neural networks to fixed-time impulsive systems.
  • To derive criteria for the existence and global exponential stability of periodic solutions.

Main Methods:

  • Utilizing the comparison principle to relate variable-time and fixed-time impulsive systems.
  • Applying Schaefer's fixed point theorem.
  • Employing inequality techniques.

Main Results:

  • Demonstrated that solutions intersect discontinuous surfaces exactly once under new assumptions.
  • Showed that variable-time impulsive neural networks can be reduced to fixed-time impulsive systems.
  • Derived sufficient criteria ensuring the existence and global exponential stability of periodic solutions.

Conclusions:

  • The study confirms that variable-time impulsive neural networks exhibit similar stability properties to fixed-time impulsive systems.
  • The derived criteria are effective in analyzing the stability of these complex neural network models.
  • A numerical example validates the proposed theoretical results.