Mathematics and Simulation of Brain-Inspired Computing: From Dynamic Models to Visual Intelligence

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 1 April 2026 | Viewed by 466

Special Issue Editors


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Guest Editor
College of Electronic Information and Engineering, Southwest University, Chongqing 400044, China
Interests: brain-like neural networks; memristors; image processing; pattern recognition; nonlinear systems

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Guest Editor
School of Artificial Intelligence, Sun Yat-Sen University, Zhuhai 519080, China
Interests: intelligent traffic flow prediction; vehicle path planning and prediction technology; trajectory data representation learning; social network representation learning and mining; entity recognition

E-Mail Website
Guest Editor
College of Electronic Information and Engineering, Southwest University, Chongqing 400044, China
Interests: computational intelligence; memristive system theory and application; chaos theory and application; impulse control theory and application; hybrid system; iterative learning control of time-delay systems

Special Issue Information

Dear Colleagues,

This Special Issue explores mathematical frameworks driving brain-inspired computing systems, focusing on dynamic computational models and their applications in visual intelligence. We seek contributions that rigorously integrate the following:

  • Mathematical modeling of neurobiological processes (e.g., coupled differential equations for spiking neurons, fractional calculus for synaptic plasticity).
  • Learning algorithms with provable properties (e.g., convergence analysis of memristor-augmented backpropagation, Lyapunov stability in neuromorphic training).
  • Optimization algorithms for energy-efficient neuromorphic architectures (e.g., stochastic gradient descent with biological constraints, gene algorithms based on memristor).
  • Computational analysis of brain-inspired systems (e.g., complexity theory for event-based vision, entropy-driven information extraction).
  • Statistical estimation in brain-like neural network vision tasks (e.g., Bayesian inference for brain-like neural network object detection, topological analysis of feature maps).
  • Machine learning theory (e.g., convergence proofs for spiking neural networks, manifold learning for neuromorphic data).

Submissions must integrate formal mathematical analysis (theorems, proofs, or quantitative benchmarks) with computer vision applications, validated through simulations or hardware experiments.

Dr. Ling Chen
Dr. Huaijie Zhu
Prof. Dr. Chuandong Li
Guest Editors

Manuscript Submission Information

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Keywords

  • memristor networks
  • nonlinear dynamics
  • neuromorphic computing
  • mathematical modeling
  • optimization theory
  • object recognition
  • stochastic learning
  • energy-efficient algorithms
  • hardware–software co-design
  • computer vision

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Published Papers (1 paper)

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Research

19 pages, 998 KB  
Article
Optimal Impulsive Control and Stabilization of Dynamic Systems Based on Quasi-Variational Inequalities
by Wenxuan Wang, Chuandong Li and Mingchen Huan
Mathematics 2025, 13(23), 3864; https://doi.org/10.3390/math13233864 - 2 Dec 2025
Viewed by 282
Abstract
In this paper, we investigate the optimal control problem regarding a class of dynamic systems, aiming to address the challenge of simultaneously ensuring cost minimization and system asymptotic stability. The theoretical framework proposed in this paper integrates the value function concept from optimal [...] Read more.
In this paper, we investigate the optimal control problem regarding a class of dynamic systems, aiming to address the challenge of simultaneously ensuring cost minimization and system asymptotic stability. The theoretical framework proposed in this paper integrates the value function concept from optimal control theory with Lyapunov stability theory. By setting the impulse cost at any finite time to be strictly positive, we exclude Zeno behavior, and a set of sufficient conditions is established that simultaneously guarantees system asymptotic stability and cost minimization based on Quasi-Variational Inequalities (QVIs). To address the challenge of solving the Hamilton–Jacobi–Bellman (HJB) equation in high-dimensional nonlinear systems, we employ an inverse optimal control framework to synthesize the strategy and its corresponding cost function. Finally, we validate the feasibility of our method by applying the theoretical results obtained to three numerical examples. Full article
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