Cellular Neural Networks, Multi-scroll Chaos And Synchronization

by Yalcin, Mustak E.; Suykens, Johan A. K.; Vandewalle, Joos P. L.

• ISBN13: 9789812561619
• ISBN10: 9812561617
• Edition: 50th
• Format: Hardcover
• Copyright: 2005-04-28
• Publisher: World Scientific Pub Co Inc

Summary

For engineering applications that are based on nonlinear phenomena, novel information processing systems require new methodologies and design principles. This perspective is the basis of the three cornerstones of this book: cellular neural networks, chaos and synchronization. Cellular neural networks and their universal machine implementations offer a well-established platform for processing spatial-temporal patterns and wave computing. Multi-scroll circuits are generalizations to the original Chua's circuit, leading to chip implementable circuits with increasingly complex attractors. Several applications make use of synchronization techniques for nonlinear systems. A systematic overview is given for Lur'e representable systems with global synchronization criteria for master-slave and mutual synchronization, robust synchronization, HV synchronization, time-delayed systems and impulsive synchronization.

Table of Contents

Preface	vii
1. Introduction	1	(14)
1.1 Nonlinear systems in engineering	1	(2)
1.2 This book	3	(2)
1.3 Chapter by chapter overview	5	(6)
1.4 Main contributions	11	(4)
2. Cellular Neural/Nonlinear Networks	15	(30)
2.1 CNN	15	(6)
2.1.1 1-D CNNs	16	(2)
2.1.2 2-D CNNs	18	(3)
2.2 CNN models	21	(6)
2.2.1 Chua-Yang CNN model	21	(1)
2.2.2 State controlled CNN (SC-CNN) model	22	(1)
2.2.3 Full-range CNN model	22	(2)
2.2.4 Reaction-diffusion CNN model	24	(1)
2.2.5 Generalized CNN models	25	(5)
2.2.5.1 A generalized CNN model: nonlinear and delay CNNs	25	(1)
2.2.5.2 Another generalized CNN model	26	(1)
2.2.5.3 A generalized CNN based on Chua's circuit	27	(1)
2.3 CNN universal machine: a visual microprocessor	27	(3)
2.4 New research directions in CNNs	30	(14)
2.4.1 Wave computing algorithm	30	(2)
2.4.2 Coupled local minimizers	32	(3)
2.4.3 Pattern formation on the ACE16k CNN Chip	35	(5)
2.4.3.1 Experimental results: Autowaves	38	(1)
2.4.3.2 Experimental results: Spiral waves	39	(1)
2.4.4 Propagation of autowaves on the inhomogeneous CNN arrays	40	(4)
2.5 Conclusion	44	(1)
3. Multi-Scroll Chaotic and Hyperchaotic Attractors	45	(60)
3.1 Chua's circuit	46	(12)
3.1.1 Chaos in Chua's circuit	47	(10)
3.1.1.1 The Shilnikov method	47	(5)
3.1.1.2 Harmonic balance method	52	(5)
3.1.2 Realization of Chua's circuit	57	(1)
3.2 Generalized Chua's circuit	58	(15)
3.2.1 Realization of n-scroll attractors from generalized Chua's circuits	63	(10)
3.2.1.1 Realization of 3- and 5-scroll attractors	64	(5)
3.2.1.2 On the realization of n-scroll attractors	69	(2)
3.2.1.3 Alternative realizations of n-scroll attractors	71	(2)
3.3 Families of scroll grid attractors	73	(18)
3.3.1 A new family of n-scroll attractors	75	(2)
3.3.2 2-D scroll grid attractors	77	(4)
3.3.3 3-D scroll grid attractors	81	(2)
3.3.4 Circuit realizations	83	(6)
3.3.5 Alternative realizations	89	(2)
3.4 Multi-scroll hyperchaotic attractors	91	(3)
3.4.1 Hyperchaotic n-scroll attractors	91	(1)
3.4.2 n-Scroll hypercube attractors	92	(2)
3.5 Scroll maps from n-scroll attractors	94	(6)
3.5.1 1-Scroll and 2-scroll maps	95	(3)
3.5.2 Circuit realization of a 1-scroll map	98	(2)
3.6 Lur'e representations	100	(4)
3.7 Conclusion	104	(1)
4. Synchronization of Chaotic Lur'e Systems	105	(50)
4.1 Synchronization	105	(4)
4.2 Master-slave synchronization: autonomous case	109	(4)
4.2.1 Full static state error feedback	109	(2)
4.2.2 Dynamic output feedback	111	(2)
4.3 Robust synchronization	113	(5)
4.3.1 Full static state error feedback	114	(2)
4.3.2 Dynamic output feedback	116	(2)
4.4 Time-delay synchronization scheme	118	(7)
4.4.1 Error system for the time-delay synchronization scheme	119	(2)
4.4.2 Delay-dependent synchronization criterion	121	(3)
4.4.3 Full static state feedback together with time delay	124	(1)
4.5 Nonlinear Hinfinity synchronization: non-autonomous case	125	(6)
4.5.1 Full static state error feedback	125	(4)
4.5.2 Dynamic output feedback	129	(2)
4.6 Robust nonlinear Hinfinity synchronization	131	(4)
4.6.1 Full static state error feedback	131	(3)
4.6.2 Dynamic output feedback	134	(1)
4.7 Impulsive synchronization	135	(3)
4.7.1 State feedback case	136	(1)
4.7.2 Measurement feedback case	137	(1)
4.8 Controller design	138	(4)
4.8.1 Master-slave synchronization	139	(1)
4.8.2 Robust synchronization	140	(1)
4.8.3 Synchronization with time-delay	140	(1)
4.8.4 Nonlinear Hinfinity synchronization	141	(1)
4.8.5 Robust nonlinear Hinfinity synchronization	141	(1)
4.9 Examples	142	(12)
4.9.1 Master-slave synchronization of two unidirectionally coupled Chua's circuits	142	(3)
4.9.2 Experimental confirmation of time-delay synchronization scheme	145	(4)
4.9.3 Experimental confirmation of nonlinear Hinfinity synchronization for Chua's circuit and 5-scroll attractors	149	(5)
4.10 Conclusion	154	(1)
5. Engineering Applications	155	(46)
5.1 Chaos in communications	155	(5)
5.1.1 Modulation and demodulation based on chaos	156	(3)
5.1.1.1 Static modulation methods	157	(1)
5.1.1.2 Dynamic modulation methods	157	(2)
5.1.2 The role of new synchronization schemes	159	(1)
5.2 Chaotic systems in optimization	160	(6)
5.2.1 Chaotic annealing	162	(1)
5.2.2 Coupled chaotic annealing	162	(2)
5.2.3 Illustrative examples	164	(2)
5.3 Random number generators and cryptography	166	(20)
5.3.1 TRNG from a double scroll attractor	168	(10)
5.3.1.1 Bit generation	170	(3)
5.3.1.2 De-skewing and setting the threshold	173	(2)
5.3.1.3 Statistical tests	175	(3)
5.3.2 Binary pseudorandom pattern generation on CNN-UM	178	(8)
5.3.2.1 PPGs from 1-D rules	180	(2)
5.3.2.2 PPGs from 2-D rules	182	(1)
5.3.2.3 Experimental results on the CNN-UM chip	182	(2)
5.3.2.4 A general comparison	184	(2)
5.4 Image/Video authentication on CNN-UM	186	(8)
5.4.1 Fragile watermarking	187	(2)
5.4.2 Fragile watermarking on the CNN-UM for image authentication	189	(1)
5.4.3 Fragile watermarking on the CNN-UM for video authentication	190	(1)
5.4.4 Experimental results on the CNN-UM chip	190	(4)
5.5 CNN template tuning	194	(4)
5.5.1 Erroneous chip behavior and template robustness	194	(2)
5.5.2 Experiments	196	(2)
5.6 Conclusions	198	(3)
6. General Conclusions and Future Work	201	(2)
Bibliography	203	(22)
Notation	225	(4)
Index	229