A Study Of Weak Attractor And Stability Theory Of Dynamical Systems
DOI:
https://doi.org/10.29304/jqcsm.2025.17.22205Keywords:
Dynamical systems, Attractor, Weak attractor, Stability theory Lyapunov stableAbstract
The topic of this paper is to concentrate on what is an attractor and show consider an exceptional class of this type of system and what is weak attractor and pullback , forward attractor and explain the difference between them and which one leads to the other through their definitions and do they have the same properties as the weak attractor. We concluded from this that every pullback attractor and forward attractor is weak attractor .Then we explain the stability theory of a dynamical system. We give characterizations of the stability theory in dynamical systems, We also study the Lyapunov stability and define this important theory, which is considered one of the most important theories , where it is ,Adynamical system is Lyapunov stable about an equilibrium point if state trajectories are confined to abounded region whenever the initial condition is chosen sufficiently close to equilibrium point .
Downloads
References
C.C Alan Fung , K. Y . Michael Wong , He Wang , and Si Wu.Dynamical systems Enhance Neural Information processing ;Gracefulness , Accuracy and Mobility . Neural Computation, 24(5) , (May 2012),pp. 1147 -1185.
Mingshan Xue , Bassam V.Atallah , and Massimo Scanziani . Equalizing excitation – inhibition ratios across visual cortical neurons . Nature , 511(7511); (july 2014),pp. 596 -600 .
H . Crauel . Random point attractors versus random set attractors Preprint , 1999 .
Ralph Bourdoukan and Sophie Deneve . Enforcing balance allows local supervised learning in spiking recurrent networks . Advance in Neural Information processing Systems, (2015), pp. 9 .
Welington de melo and Sebastian van strien. One dimensional dynamics .springer- verlag,Berlin,1993.
D.N. cheban,Global Attractors of Non-autonomous Dissipative Dynamical systems.World Scientific,2004.
M.Scheutzow , Attractors for ergodic and monotone random dynamical systems , in seminar on stochastic Analysis ,Random Fields and Applications V, R. Dalang ,M.Dozzi,and F. Russo (eds) , Birkhauser Verlag (2008). PP.331-344.
L.F Abbott , Brian Depasquale , and Raoul –Martin Memmesheimer . Building functional networks of spiking model neurons . Nature Neuroscience , 19(3); (March 2016),pp. 350-355.
Scheinerman ,Edward. Invitation to Dynamical systems . Web.12 may 2014.
. Mehall , kevin . Vector Fields , Vector Field On line Graphing. Web.25, March 2015 .
Gengshuo |Tian , Shangyang Li , Tiejun Huang , and Si Wu . Excitation – Inhibition Balanced Neural Networks for Fast Signal Detection . Frontiers in Computational Neuroscience , 14;79, September 2020 .
V.V Chepyzhov , Approximating the trajectory attractor of the 3D Navier ,stokes system using various models of fluid dynamics , Sb . Math , 207(2016) ,pp.610 -638. Doi:10.1070 /Sm8549 .
C.Amrouche ,L.C.Berselli , R.Lewandowski and D.D.Nguyen,Turbulent flows as generalized Kelvin /Voigh materials :Modeling and analysis , nonlinear Anal . 196 (2020), 111790,24 pp. doi :10.1016/j.na.2020.111790 .
K.R.Verma,Modern Control theory,CBS publishers and Distributors Pvt ltd 2018.
Chaoming Wang , Xiaoyu Chen , Tianqiu Zhaang , and Si Wu. Brainpy ;A fiexible ,integrative , efficient , and extensible framework towards general purpose brain dynamics programming ,preprint , Neuroscience , October 2022 .
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Ansam Abbass Ali, Haneen Zaghair Hasan
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
