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

IVi

Vii

Viii

1 INTRODUCTION

1.1 GENERAL

1.2 OVERVIEW

11

3

2 LITERATURE SURVEY6

3 SYSTEM ANALYSIS

3.1 EXISTING SYSTEM

3.2 PROPOSED SYSTEM

1111

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

ii

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

1414

14

141415

16

17

19

19

20

20

4.6C# LANGUAGE

4.7TECHNICAL FEASIBILITY

4.8OPERATIONAL FEASIBILITY

4.9ECONOMIC FEASIBILITY

4.10HARDWARE REQUIRED

4.11SOFTWARE REQUIRED2123

24

25

25

25

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

28

28

28

28

28

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

29

29

29

29

29

7 IMPLEMENTATION

7.1 GENERAL

7.2 IMPLEMENTATION

7.3 REQUIREMENTS GATHERING

7.4 DESIGN

7.5 SAMPLE CODING3535

35

35

36

37

8 SNAPSHOTS

8.1 GENERAL

8.2 SCREENSHOTS

8282

82

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

iv

8686

86

87

87

8889

10 CONCLUSION AND FUTURE ENHANCEMETS91

11 CONCLUSION91

12 FUTURE ENHANCEMENT

92

13 REFERENCES93

v

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

viii