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STABILITY ANALYSIS OF CONTINOUS-TIME RECURRENT NEURAL NETWORKSA PROJECT REPORTSubmitted byK.BALAJI (822411104301)S.SUNDHARRAJAN (822411104302)
in partial fulfillment for the award of the degree
of
BACHELOR OF ENGINEERING
in
COMPUTER SCIENCE AND ENGINEERING
MRK INSTITUTE OF TECHNOLOGY, KATTUMANNARKOIL
ANNA UNIVERSITY::CHENNAI 600 025
APRIL 2015ANNA UNIVERSITY: CHENNAI 600 025
BONAFIDE CERTIFICATE
Certified that this project report STABILITY ANALYSIS OF CONTINOUS-TIME RECURRENT NEURAL NETWORKS is the bonafide work of K.BALAJI (822411104301), S.SUNDHARRAJAN (822411104302) who carried out the project work under my supervision.
SIGNATURE
SIGNATURE
Ms.R.SEETHALAKSHMI. B.E.,M.Tech., Mr.S.RAMALINGAM.,M.E.,
HEAD OF THE DEPARTMENT,
SUPERVISIOR,
Department of CSE,
Assistant Professor,
MRK Institute of Technology,
Department of CSE,
Kattumannarkoil-608 301.
MRK Institute of Technology,
Kattumannarkoil-608 301.
Submitted for the project work (CS2451) and Viva-Voce Examination held on .. at MRK Institute of Technology, Kattumannarkoil.
INTERNAL EXAMINER
EXTERNAL EXAMINER
ABSTRACTDynamical neural networks are being increasingly employed in a variety of different contexts, including as simple model nervous systems for autonomous agents. For this reason, there is a growing need for a comprehensive understanding of their dynamical properties. Using a combination of elementary analysis and numerical experiments, this paper begins a systematic study of the dynamics of continuous-time recurrent neural networks. Specifically, a fairly complete description of the possible dynamical behavior and bifurcations of 1- and 2-neuron circuits is given, along with a few specific results for larger networks. This analysis provides both qualitative insight and, in many cases, quantitative formulae for predicting the dynamical behavior of particular circuits and how that behavior changes as network parameters are varied. These results demonstrate that even small circuits are capable of a rich variety of dynamical behavior (including chaotic dynamics). An approach to understanding the dynamics of circuits with time-varying inputs is also presented. Finally, based on this analysis, several strategies for focusing evolutionary searches into fruitful regions of network parameter space are suggested.iTABLE OF CONTENTSCHAPTER NOTITLE
PAGE NO
ABSTRACT
LIST OF FIGURES
LIST OF SYMBOLS
LIST OF ABBREVIATIONS
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1 INTRODUCTION
1.1 GENERAL
1.2 OVERVIEW
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3
2 LITERATURE SURVEY6
3 SYSTEM ANALYSIS
3.1 EXISTING SYSTEM
3.2 PROPOSED SYSTEM
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12
4 REQUIREMENTS
4.1 GENERAL
4.2 SOFTWARE TOOLS
SOFTWARE SPECIFICATION
4.3 GENERAL
4.4 LANGUAGE REPORT
4.5. NET FRAMEWORK
4.5.1 GENERAL
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4.5.2 Components of the .Net framework
4.5.3Common Type System (CIS)
4.5.4Microsoft Intermediate Language (MSIL)
4.5.5Just In Time (JIT)
4.5.6 .Net Class Library
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4.6C# LANGUAGE
4.7TECHNICAL FEASIBILITY
4.8OPERATIONAL FEASIBILITY
4.9ECONOMIC FEASIBILITY
4.10HARDWARE REQUIRED
4.11SOFTWARE REQUIRED2123
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5 METHODOLOGIES
5.1 PROBLEM DEFINITION
5.2 MODULES DESCRIPTION5.2.1 SERVER MODULE
5.2.2 PATH SET MODULE
5.2.3 PACKET TRANSACTION MODULE
5.2.4 CLIENT MODULE2627
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6 DESIGN PHASE6.1 GENERAL
iii6.2 UML DIAGRAMS6.2.1 USE CASE DIAGRAM
6.2.2 CLASS DIAGRAM
6.2.3 SEQUENCE DIAGRAM
6.2.4 ACTIVITY DIAGRAM29
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7 IMPLEMENTATION
7.1 GENERAL
7.2 IMPLEMENTATION
7.3 REQUIREMENTS GATHERING
7.4 DESIGN
7.5 SAMPLE CODING3535
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8 SNAPSHOTS
8.1 GENERAL
8.2 SCREENSHOTS
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9 TESTING
9.1 TESTING
9.2 INTEGRATION TESTING
9.2.1 BOTTOM-UP TESTING
9.2.2 TOP-DOWN TESTING
9.3 BLACK BOX TESTING
9.4 WHITE BOX TESTING
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10 CONCLUSION AND FUTURE ENHANCEMETS91
11 CONCLUSION91
12 FUTURE ENHANCEMENT
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13 REFERENCES93
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LIST OF FIGURESFIG NOFIGURE NAMEPAGE NO
4.5Components Of The .NET Framework
17
6.2Use Case Diagram 30
6.3Activity Diagram 32
6.4Sequence Diagram 33
6.5Class Diagram 34
8.1Home Page82
8.2Channel-1 & Channel-2 File Transmit83
8.3Start Server Diagram83
8.4Sender to Receiver Side Location84
8.5Acknowledgement Receive84
8.6Average Delay Probabilities85
viLIST OF SYMBOLSSYMBOLSYMBOL NAMEDESCRIPTION
ACTORActor is anything that interacts with a usecase.
Initial stateIt represents the starting point of the flow.
Final stateIt represents the end of the diagram
StateRepresents the state of process.
Event/actionRepresents the action or transition in the flow.
viiLIST OF ABBREVATIONABBREVATIONDESCRIPTION
CTRNNsContinuous-Time Recurrent Neural Networks
HSPDAHigh Speed Downlink Packet Access
UEUser Equipment
CQIChannel Quality Indicator
HS-PDSCHHigh Speed Physical Downlink Shared Channel
BLERBlock Error Rate
TFRCTransport Format Resource Combination
ACK/NACKAcknowledgement/Nyquist Acknowledgement
SAAStochastic Approximation Algorithm
MSILMicrosoft Intermediate Language
JITJust-In Time
CLRCommon Language Runtime
CTSCommon Type System
ILIntermediate Language
DBADatabase Administrator
ICTIn-Circuit Testing
AOIAutomated Optical Inspection
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