Cellular Neural Networks: Space-Dependent Template, Mosaic Patterns and Spatial Chaos

نویسندگان

  • Jonq Juang
  • Shih-Feng Shieh
  • Larry Turyn
چکیده

We consider a Cellular Neural Network (CNN) with a bias term in the integer lattice Z on the plane Z. We impose a space-dependent coupling (template) appropriate for CNN in the hexagonal lattice on Z. Stable mosaic patterns of such CNN are completely characterized. The spatial entropy of a (p1, p2)-translation invariant set is proved to be well-defined and exists. Using such a theorem, we are also able to address the complexities of resulting mosaic patterns.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Exact Number of Mosaic Patterns in Cellular Neural Networks

This work investigates mosaic patterns for the one-dimensional cellular neural networks with various boundary conditions. These patterns can be formed by combining the basic patterns. The parameter space is partitioned so that the existence of basic patterns can be determined for each parameter region. The mosaic patterns can then be completely characterized through formulating suitable transit...

متن کامل

Cellular Neural Networks: Local Patterns for General Templates

This work investigates the mosaic local patterns for cellular neural networks with general templates. Our results demonstrate that the set of templates can be divided into many finite regions. In each region, the same family of local patterns can be generated. Conversely, our results further demonstrate that some templates can realize a family of local patterns which can be linearly separated b...

متن کامل

Cellular Neural Networks: Mosaic Pattern and Spatial Chaos

We consider a cellular neural network (CNN) with a bias term z in the integer lattice Z on the plane R2. We impose a symmetric coupling between nearest neighbors, and also between next-nearest neighbors. Two parameters, a and ε, are used to describe the weights between such interacting cells. We study patterns that can exist as stable equilibria. In particular, the relationship between mosaic p...

متن کامل

Abundance of Mosaic Patterns for CNN with Spatially Variant Templates

This work investigates the complexity of one-dimensional cellular neural network mosaic patterns with spatially variant templates on finite and infinite lattices. Various boundary conditions are considered for finite lattices and the exact number of mosaic patterns is computed precisely. The entropy of mosaic patterns with periodic templates can also be calculated for infinite lattices. Further...

متن کامل

Influence of Boundary Conditions on Pattern Formation and Spatial Chaos in Lattice Systems

This work elucidates the spatial structure of lattice dynamical systems, which is represented by equilibria of the systems. On a finite lattice, various boundary conditions are imposed. The effect from these boundary conditions on formation of pattern as well as spatial complexity, as the lattice size tends to infinity, is investigated. Two general propositions are proposed as a criteria to dem...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • I. J. Bifurcation and Chaos

دوره 12  شماره 

صفحات  -

تاریخ انتشار 2002