Cellular Neural Networks, Multi-Scroll Chaos and Synchronization

The following sections are included:

• Preface

• Contents

The following sections are included:

• Nonlinear systems in engineering

• This book

• Chapter by chapter overview

• Main contributions

The following sections are included:

• CNN
  • 1-D CNNs
  • 2-D CNNs

• CNN models
  • Chua-Yang CNN model
  • State controlled CNN (SC-CNN) model
  • Full-range CNN model
  • Reaction-diffusion CNN model
  • Generalized CNN models
    • A generalized CNN model: nonlinear and delay CNNs
    • Another generalized CNN model
    • A generalized CNN based on Chua's circuit

• CNN universal machine: a visual microprocessor

• New research directions in CNNs
  • Wave computing algorithm
  • Coupled local minimizers
  • Pattern formation on the ACE16k CNN Chip
    • Experimental results: Autowaves
    • Experimental results: Spiral waves
  • Propagation of autowaves on the inhomogeneous CNN arrays

• Conclusion

The following sections are included:

• Chua's circuit
  • Chaos in Chua's circuit
    • The Shilnikov method
    • Harmonic balance method
  • Realization of Chua's circuit

• Generalized Chua's circuit
  • Realization of n-scroll attractors from generalized Chua's circuits
    • Realization of 3- and 5-scroll attractors
    • On the realization of n-scroll attractors
    • Alternative realizations of n-scroll attractors

• Families of scroll grid attractors
  • A new family of n-scroll attractors
  • 2-D scroll grid attractors
  • 3-D scroll grid attractors
  • Circuit realizations
  • Alternative realizations

• Multi-scroll hyperchaotic attractors
  • Hyperchaotic n-scroll attractors
  • n-Scroll hypercube attractors

• Scroll maps from n-scroll attractors
  • 1-Scroll and 2-scroll maps
  • Circuit realization of a 1-scroll map

• Lur'e representations

• Conclusion

The following sections are included:

• Synchronization

• Master-slave synchronization: autonomous case
  • Full static state error feedback
  • Dynamic output feedback

• Robust synchronization
  • Full static state error feedback
  • Dynamic output feedback

• Time-delay synchronization scheme
  • Error system for the time-delay synchronization scheme
  • Delay-dependent synchronization criterion
  • Full static state feedback together with time delay

• Nonlinear H_∞ synchronization: non-autonomous case
  • Full static state error feedback
  • Dynamic output feedback

• Robust nonlinear H_∞ synchronization
  • Full static state error feedback
  • Dynamic output feedback

• Impulsive synchronization
  • State feedback case
  • Measurement feedback case

• Controller design
  • Master-slave synchronization
  • Robust synchronization
  • Synchronization with time-delay
  • Nonlinear H_∞ synchronization
  • Robust nonlinear H_∞ synchronization

• Examples
  • Master-slave synchronization of two unidirectionally coupled Chua's circuits
  • Experimental confirmation of time-delay synchronization scheme
  • Experimental confirmation of nonlinear H_∞ synchronization for Chua's circuit and 5-scroll attractors

• Conclusion

The following sections are included:

• Chaos in communications
  • Modulation and demodulation based on chaos
    • Static modulation methods
    • Dynamic modulation methods
  • The role of new synchronization schemes

• Chaotic systems in optimization
  • Chaotic annealing
  • Coupled chaotic annealing
  • Illustrative examples

• Random number generators and cryptography
  • TRNG from a double scroll attractor
    • Bit generation
    • De-skewing and setting the threshold
    • Statistical tests
  • Binary pseudorandom pattern generation on CNN-UM
    • PPGs from 1-D rules
    • PPGs from 2-D rules
    • Experimental results on the CNN-UM chip
    • A general comparison

• Image/Video authentication on CNN-UM
  • Fragile watermarking
  • Fragile watermarking on the CNN-UM for image authentication
  • Fragile watermarking on the CNN-UM for video authentication
  • Experimental results on the CNN-UM chip

• CNN template tuning
  • Erroneous chip behavior and template robustness
  • Experiments

• Conclusions

This book consisted of three cornerstones: cellular neural networks, chaos and synchronization. While nonlinear phenomena were often to be avoided in classical engineering designs, novel information processing systems try to make use of nonlinear effects for creating new applications, inspired on new design principles…

The following sections are included:

• Bibliography

• Notation

• Index