Remarks on the Mathematical Modeling of Gene and Neuronal Networks by Ordinary Differential Equations

被引：1
|
作者：
Ogorelova, Diana [1 ]
Sadyrbaev, Felix [1 ,2 ]
机构：
[1] Daugavpils Univ, Fac Nat Sci & Math, Vienibas St 13, LV-5401 Daugavpils, Latvia
[2] Univ Latvia, Inst Math & Comp Sci, Rainis Blvd 29, LV-1459 Riga, Latvia
来源：
AXIOMS | 2024年 / 13卷 / 01期
关键词：
neuronal networks; dynamical systems; artificial networks; critical points; attractors; DYNAMICAL-SYSTEMS; NEURAL-NETWORKS;
D O I：
10.3390/axioms13010061
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the theory of gene networks, the mathematical apparatus that uses dynamical systems is fruitfully used. The same is true for the theory of neural networks. In both cases, the purpose of the simulation is to study the properties of phase space, as well as the types and the properties of attractors. The paper compares both models, notes their similarities and considers a number of illustrative examples. A local analysis is carried out in the vicinity of critical points and the necessary formulas are derived.
引用
收藏
页数：16
相关论文
共 50 条
  • [31] Stable attractors for neural networks classification via ordinary differential equations (SA-nODE)
    Marino, Raffaele
    Buffoni, Lorenzo
    Chicchi, Lorenzo
    Giambagli, Lorenzo
    Fanelli, Duccio
    MACHINE LEARNING-SCIENCE AND TECHNOLOGY, 2024, 5 (03):
  • [32] DEEP NEURAL NETWORKS WITH FLEXIBLE COMPLEXITY WHILE TRAINING BASED ON NEURAL ORDINARY DIFFERENTIAL EQUATIONS
    Luo, Zhengbo
    Kamata, Sei-ichiro
    Sun, Zitang
    Zhou, Weilian
    2021 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP 2021), 2021, : 1690 - 1694
  • [33] Some remarks on fuzzy differential equations via differential inclusions
    Chalco-Cano, Y.
    Roman-Flores, H.
    FUZZY SETS AND SYSTEMS, 2013, 230 : 3 - 20
  • [34] Partial Differential Equations Numerical Modeling Using Dynamic Neural Networks
    Fuentes, Rita
    Poznyak, Alexander
    Chairez, Isaac
    Poznyak, Tatyana
    ARTIFICIAL NEURAL NETWORKS - ICANN 2009, PT II, 2009, 5769 : 552 - +
  • [35] Fuzzy Differential Equations for Nonlinear System Modeling with Bernstein Neural Networks
    Jafari, Raheleh
    Yu, Wen
    Li, Xiaoou
    IEEE ACCESS, 2016, 4 : 9428 - 9436
  • [36] Stability of functional differential equations with variable impulsive perturbations via generalized ordinary differential equations
    Afonso, S. M.
    Bonotto, E. M.
    Federson, M.
    Gimenes, L. P.
    BULLETIN DES SCIENCES MATHEMATIQUES, 2013, 137 (02): : 189 - 214
  • [37] DIRICHLET SERIES FOR DYNAMICAL SYSTEMS OF FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS
    Wang, Bing
    Iserles, Arieh
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2014, 19 (01): : 281 - 298
  • [38] Near-optimal control of dynamical systems with neural ordinary differential equations
    Boettcher, Lucas
    Asikis, Thomas
    MACHINE LEARNING-SCIENCE AND TECHNOLOGY, 2022, 3 (04):
  • [39] Infinitely many periodic solutions of ordinary differential equations
    He, Yong
    Xu, Bo
    APPLIED MATHEMATICS LETTERS, 2014, 38 : 149 - 154
  • [40] Remotely Almost Periodic Solutions of Ordinary Differential Equations
    Maulen, C.
    Castillo, S.
    Kostic, M.
    Pinto, M.
    JOURNAL OF MATHEMATICS, 2021, 2021
12345