Location and stability of the high-gain equilibria of nonlinear neural networks

IEEE Transactions on Neural Networks
M Vidyasagar

Abstract

The author analyzes the number, location, and stability behavior of the equilibria of arbitrary nonlinear neural networks without resorting to energy arguments based on assumptions of symmetric interactions or no self-interactions. The class of networks studied consists of very general continuous-time continuous-state (CTCS) networks that contain the standard Hopfield network as a special case. The emphasis is on the case where the slopes of the sigmoidal nonlinearities become larger and larger.

References

May 1, 1984·Proceedings of the National Academy of Sciences of the United States of America·J J Hopfield
Apr 1, 1982·Proceedings of the National Academy of Sciences of the United States of America·J J Hopfield
Nov 1, 1986·Physical Review A: General Physics·L PersonnazG Dreyfus

Citations

Jan 1, 1997·Artificial Intelligence in Medicine·E B ReateguiB F Leao
Dec 1, 1995·Journal of Behavior Therapy and Experimental Psychiatry·W W Tryon
Apr 20, 2002·Mathematical Biosciences·Julien Arino, Jean-Luc Gouzé
Dec 7, 2011·Theoretical Population Biology·Richard RebarberStuart Townley
Jul 19, 2011·Neural Networks : the Official Journal of the International Neural Network Society·Xiaoyang LiuWenlian Lu
Feb 6, 2009·ISA Transactions·Vahid Meigoli, Seyyed Kamaleddin Yadavar Nikravesh
Jul 1, 1995·Molecular Medicine Today·P M Rowe
Mar 1, 1995·Comprehensive Psychiatry·M Spitzer
Feb 7, 2008·IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society·P Liang, K Xiong
Jan 1, 1996·IEEE Transactions on Neural Networks·P B Watta, M H Hassoun
Feb 7, 2008·IEEE Transactions on Neural Networks·F Shiratani, K Yamamoto
Feb 6, 2008·IEEE Transactions on Neural Networks·B D Calvert, C A Marinov
Feb 6, 2008·IEEE Transactions on Neural Networks·D L Lee
Jan 1, 1996·IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society·J S DrayeG A Libert
Feb 5, 2008·IEEE Transactions on Neural Networks·M Forti
Apr 11, 2006·Journal of Theoretical Biology·J R C PiqueiraL H A Monteiro
Aug 13, 2015·Neural Networks : the Official Journal of the International Neural Network Society·Weiqiang GongJinde Cao
Sep 27, 2016·Mathematical Biosciences·Alina I Doban, Mircea Lazar
Dec 3, 2008·Chaos·He Huang, Gang Feng
Apr 27, 2010·PLoS Computational Biology·Giovanni RussoEduardo D Sontag
Nov 12, 2005·Biological cybernetics·E BurdetM Kawato
Apr 6, 2007·BMC Systems Biology·Chunguang LiKazuyuki Aihara
Jul 4, 2019·Journal of the Royal Society, Interface·Alejandro F VillaverdeJulio R Banga

Related Concepts

Symmetrical
Location
Drug Interactions
Neural Network Simulation
Continuous Capillary

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Neural Activity: Imaging

Imaging of neural activity in vivo has developed rapidly recently with the advancement of fluorescence microscopy, including new applications using miniaturized microscopes (miniscopes). This feed follows the progress in this growing field.

The Tendon Seed Network

Tendons are rich in the extracellular matrix and are abundant throughout the body providing essential roles including structure and mobility. The transcriptome of tendons is being compiled to understand the micro-anatomical functioning of tendons. Discover the latest research pertaining to the Tendon Seed Network here.

Myocardial Stunning

Myocardial stunning is a mechanical dysfunction that persists after reperfusion of previously ischemic tissue in the absence of irreversible damage including myocardial necrosis. Here is the latest research.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Incretins

Incretins are metabolic hormones that stimulate a decrease in glucose levels in the blood and they have been implicated in glycemic regulation in the remission phase of type 1 diabetes. Here is the latest research.

Chromatin Regulation and Circadian Clocks

The circadian clock plays an important role in regulating transcriptional dynamics through changes in chromatin folding and remodelling. Discover the latest research on Chromatin Regulation and Circadian Clocks here.

Long COVID-19

“Long Covid-19” describes illness in patients who are reporting long-lasting effects of the SARS-CoV-19 infection, often long after they have recovered from acute Covid-19. Ongoing health issues often reported include low exercise tolerance and breathing difficulties, chronic tiredness, and mental health problems such as post-traumatic stress disorder and depression. This feed follows the latest research into Long Covid.

Spatio-Temporal Regulation of DNA Repair

DNA repair is a complex process regulated by several different classes of enzymes, including ligases, endonucleases, and polymerases. This feed focuses on the spatial and temporal regulation that accompanies DNA damage signaling and repair enzymes and processes.