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An Exact and Direct Analytical Method for the Design of Optimally Robust CNN Templates
 IEEE TRANS. CIRCUITS & SYST.I
, 1999
"... In this paper, we present an analytical design approach for the class of bipolar cellular neural networks (CNN's) which yields optimally robust template parameters. We give a rigorous definition of absolute and relative robustness and show that all welldefined CNN tasks are characterized by a ..."
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Cited by 5 (2 self)
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In this paper, we present an analytical design approach for the class of bipolar cellular neural networks (CNN's) which yields optimally robust template parameters. We give a rigorous definition of absolute and relative robustness and show that all welldefined CNN tasks are characterized by a finite set of linear and homogeneous inequalities. This system of inequalities can be analytically solved for the most robust template by simple matrix algebra. For the relative robustness of a task, a theoretical upper bound exists and is easily derived, whereas the absolute robustness can be arbitrarily increased by template scaling. A series of examples demonstrates the simplicity and broad applicability of the proposed method.
Cluster Synchronization in Threedimensional Lattices of Diffusively Coupled Oscillators
 Int. J. of Bifurcation and Chaos
"... Cluster synchronization modes of continuous time oscillators that are diffusively coupled in a threedimensional (3D) lattice are studied in the paper via the corresponding linear invariant manifolds. Depending in an essential way on the number of oscillators composing the lattice in three volume d ..."
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Cited by 3 (0 self)
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Cluster synchronization modes of continuous time oscillators that are diffusively coupled in a threedimensional (3D) lattice are studied in the paper via the corresponding linear invariant manifolds. Depending in an essential way on the number of oscillators composing the lattice in three volume directions, the set of possible regimes of spatiotemporal synchronization is examined. Sufficient conditions of the stability of cluster synchronization are obtained analytically for a wide class of coupled dynamical systems with complicated individual behavior. Dependence of the necessary coupling strengths for the onset of global synchronization on the number of oscillators in each lattice direction is discussed and an approximative formula is proposed. The appearance and order of stabilization of the cluster synchronization modes with increasing coupling between the oscillators are revealed for 2D and 3D lattices of coupled Lur’e systems and of coupled Rössler oscillators.
Dynamic Circular Cellular Networks for Adaptive Smoothing of MultiDimensional Signals
 In IEEE International Workshop on Cellular Neural Networks and their Applications
, 1998
"... In [10] a theoretical framework for locallyadaptive smoothing of multidimensional data was presented. Based on this framework we introduce a hardware efficient architecture suitable for mixedmode VLSI implementation. Substantial shortcomings of analogue implementations are overcome by connecting a ..."
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Cited by 1 (1 self)
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In [10] a theoretical framework for locallyadaptive smoothing of multidimensional data was presented. Based on this framework we introduce a hardware efficient architecture suitable for mixedmode VLSI implementation. Substantial shortcomings of analogue implementations are overcome by connecting all cells in a circular structure: i) influence of process parameter deviation ii) limited number of cells iii) input/output bottleneck. The connections between the analogue cells and the cells themselves are dynamically reconfigured. This results in a nonlinear adaptive filter kernel which is shifted virtually over the signal vector of infinite length. A 1d prototype with 32 cells has been fabricated using 0.8¯m CMOStechnology. The chip is fully functional with an overall error less than 1%; experimental results are presented in this paper.
Bifurcations and chaos in twocells Cellular Neural Networks with periodic inputs
, 2003
"... This study investigates bifurcations and chaos in twocells Cellular Neural Networks (CNN) with periodic inputs. Without the inputs, the time periodic solutions are obtained for template A =[r, p, s] with p>1, r>p − 1and−s>p − 1. The number of periodic solutions can be proven to be no more ..."
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This study investigates bifurcations and chaos in twocells Cellular Neural Networks (CNN) with periodic inputs. Without the inputs, the time periodic solutions are obtained for template A =[r, p, s] with p>1, r>p − 1and−s>p − 1. The number of periodic solutions can be proven to be no more than two in exterior region. The input is b sin 2πt/T with period T>0 and amplitude b>0. The typical trajectories Γ(b, T, A) and their ωlimit set ω(b, T, A) vary with b, T and A are considered. The asymptotic limit cycles Λ∞(T,A)withperiod T of Γ(b, T, A) are obtained as b →∞. When T0 ≤ T ∗ 0 (given in 6.10), Λ ∞ and −Λ ∞ can be separated. The onset of chaos can be induced by crises of ω(b, T, A) and−ω(b, T, A) for suitable T and b. The ratio A(b) =aT (b)/a1(b), of largest amplitude a1(b) and amplitude of the Tmode of the Fast Fourier Transform (FFT) of Γ(b, T, A), can be used to compare the strength of sustained periodic cycle Λ0(A) and the inputs. When A(b) ≪ 1, Λ0(A) dominates and the attractor
Mosaic Solutions and Spatial Entropy for a Class of Neural Networks Models
"... . In this article, we present a lattice differential equation model for a class of neural networks. We define a subset of the equilibrium solutions we call mosaic equilibrium solutions. Existence and stability theorems are proved for mosaic equilibrium solutions. Regions of stability are defined and ..."
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. In this article, we present a lattice differential equation model for a class of neural networks. We define a subset of the equilibrium solutions we call mosaic equilibrium solutions. Existence and stability theorems are proved for mosaic equilibrium solutions. Regions of stability are defined and spatial entropy calculations, as a measure of the complexity of the system, are presented that give insights in to the effects of spatial coupling. 1. Introduction. Neural networks are computational models characterized by patterns of weighted interconnections between neurons or cells. The method of determining the weights is called a training algorithm which resets the weights in accordance with some activation function. The result is a system which trains itself to recognize patterns or emulate functions. Traditional nets such as the Hopfield Net and the standard Backpropagation Neural Network have been intriguing to many disciplines. Although training can be slow, the resulting network ...