Solutions For Cellular Neural Networks Research Articles

Stability and Existence of Periodic Solutions of Periodic Cellular Neural Networks with Time-Vary Delays

By using the continuation theorem of Mawhins coincidence degree theory and constructing a suitable Lyapunov function, some new sufficient conditions are obtained ensuring existence and global asymptotical stability of periodic solution of cellular neural networks with periodic coefficients and delays, which do not require the activation functions to be differentiable and monotone nondecreasing. A numerical example is given to illustrate that the criteria are feasible. These results are helpful to design globally asymptotically stable and periodic oscillatory cellular neural networks.

Existence and global exponential stability of periodic solution of CNNs with impulses

Abstract Sufficient conditions are obtained for the existence and global exponential stability of a unique periodic solution of cellular neural networks with variable time delays and impulses by using Mawhin’s continuation theorem of coincidence degree and by means of a method based on delay differential inequality.

Existence of periodic solutions for cellular neural networks with complex deviating arguments

In this paper, cellular neural networks with complex deviating arguments are considered. Sufficient conditions for the existence of the periodic solutions are established by using the coincidence degree theorem. The results of this paper are new and complement previously known results.

Existence and exponential stability of almost periodic solutions for cellular neural networks with mixed delays

Abstract In this paper cellular neural networks with mixed delays are considered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using fixed point theorem, Lyapunov functional method and differential inequality technique. The results of this paper are new and they complement previously known results.

Existence and Global Exponential Stability of Almost Periodic Solution for Cellular Neural Networks With Variable Coefficients and Time-Varying Delays

In this paper, we study cellular neural networks with almost periodic variable coefficients and time-varying delays. By using the existence theorem of almost periodic solution for general functional differential equations, introducing many real parameters and applying the Lyapunov functional method and the technique of Young inequality, we obtain some sufficient conditions to ensure the existence, uniqueness, and global exponential stability of almost periodic solution. The results obtained in this paper are new, useful, and extend and improve the existing ones in previous literature.

Existence and exponential stability of periodic solutions for cellular neural networks with time-varying delays

In this Letter cellular neural networks with time-varying delays are considered. Sufficient conditions for the existence and exponential stability of the periodic solutions are established by using the coincidence degree theorem and differential inequality technique. The results of this Letter are new and they complement previously known results.

Existence and exponential stability of almost periodic solutions for cellular neural networks with time-varying delays

In this Letter cellular neural networks with time-varying delays are considered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this Letter are new and they complement previously known results.

Global exponential stability and periodicity of cellular neural networks with variable delays

The Letter presents sufficient conditions ensuring the global exponential stability and existence of the periodic solution for cellular neural networks with variable delays. The results allow for the consideration of all unbounded neuron activation functions (but not necessarily surjective), in particular, can analyze the exponential stability and periodicity for the linear cellular neural networks. The work provides one such method which can be applied to cellular neural networks systems with variable delays. The method, based on the theory of fixed point and differential inequality technique. The applicability of the present results is demonstrated by two examples.

Existence and global exponential stability of periodic solution of cellular neural networks with time-varying delays

By using the continuation theorem of Mawhin's coincidence degree theory and Gronwall's inequality, some new sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution of cellular neural networks with periodic coefficients and delays. These results are helpful to design globally exponentially stable and oscillatory cellular neural networks.

CHAOTIC STATIONARY SOLUTIONS OF CELLULAR NEURAL NETWORKS

This study describes the chaotic stationary solutions of one-dimensional Cellular Neural Networks (CNN) without inputs with a specific term by applying the iteration map method. Under perfectly determined specific parameters, the map which corresponds to the stationary solution of CNN is two-dimensional and has a hyperbolic invariant Cantor set on which it is topologically conjugate to a two-sided shift of symbols space. The used main tool is the Conley–Moser conditions.

Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays

This paper is devoted to the existence and global attractivity of almost periodic solution for a class of cellular neural network with distributed delays and variable coefficients. Some sufficient conditions ensuring the existence and global attractivity of almost periodic solution are derived by employing Banach fixed point theory and using differential inequality technique. The results allow for the consideration of all unbounded neuron signal functions (but not necessarily surjective). Thus, these conditions obtained have highly important significance in designs and applications of the networks. We extend and improve previously known results. An example is also worked out to demonstrate the advantages of our results.

On camel-like traveling wave solutions in cellular neural networks

This paper is concerned with the existence of camel-like traveling wave solutions of cellular neural networks distributed in the one-dimensional integer lattice Z 1 . The dynamics of each given cell depends on itself and its nearest m left neighbor cells with instantaneous feedback. The profile equation of the infinite system of ordinary differential equations can be written as a functional differential equation in delayed type. Under appropriate assumptions, we can directly figure out the solution formula with many parameters. When the wave speed is negative and close to zero, we prove the existence of camel-like traveling waves for certain parameters. In addition, we also provide some numerical results for more general output functions and find out oscillating traveling waves numerically.

New results concerning exponential stability and periodic solutions of delayed cellular neural networks

Employing Young inequality firstly and general Lyapunov functional, the author studies further global exponential stability and the existence of periodic solutions of cellular neural networks with delays in this Letter. A family of simple sufficient conditions is given for checking global exponential stability and the existence of periodic solutions of cellular neural networks with delays. The results extend and improve the earlier publications

Existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients

By combining the theory of the exponential dichotomy and Liapunov function, we study the existence and attractivity of almost periodic solutions for cellular neural networks (CNNs) with distributed delays and variable coefficients dx i dt =−b i(t)x i(t)+∑ j=1 na ij(t)f j(x j(t))+∑ j=1 nb ij(t)f j μ j∫ 0 ∞k ij(u)x j(t−u) du +I i(t). We obtain some sufficient conditions to ensure that for the networks there exists a unique almost periodic solution, and all its solutions converge to such an almost periodic solution. An example is given to illustrate that the conditions of our results are feasible.

Global exponential stability and existence of periodic solutions of CNNs with delays

In this Letter, we establish general sufficient conditions for global exponential stability and existence of periodic solutions of a class of cellular neural networks (CNNs) with delays. The key to proving the sufficient conditions is the construction of a new Lyapunov functional. An elementary inequality, which may be of independent interest, has been employed in the proof. Checking the sufficient conditions is often reduced to checking some algebraic relations among certain set of parameter. Our sufficient conditions recover the known results in literature as special cases. Finally, we give two examples to illustrate the usage of our main results.

Global exponential stability and periodic solutions of cellular neural networks with delay.

In this paper, some sufficient conditions for the global exponential stability and the existence of periodic solutions of cellular neural networks with delay (DCNN) model are obtained by means of a Lyapunov functional approach. These conditions can be used to design globally stable DCNN's and periodic oscillatory DCNN's and thus have important significance in both theory and applications.

On exponential stability and periodic solutions of CNNs with delays

In this Letter, the author analyses further problems of global exponential stability and the existence of periodic solutions of cellular neural networks with delays (DCNNs). Some simple and new sufficient conditions are given ensuring global exponential stability and the existence of periodic solutions of DCNNs by applying some new analysis techniques and constructing suitable Lyapunov functionals. These conditions have important leading significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs and are weaker than those in the earlier works [Phys. Rev. E 60 (1999) 3244], [J. Comput. Syst. Sci. 59 (1999)].

TRAVELING WAVES IN CELLULAR NEURAL NETWORKS

In this paper, we study the structure of traveling wave solutions of Cellular Neural Networks of the advanced type. We show the existence of monotone traveling wave, oscillating wave and eventually periodic wave solutions by using shooting method and comparison principle. In addition, we obtain the existence of periodic wave train solutions.

VLSI design of optimization and image processing cellular neural networks

Detailed design of a current-mode cellular neural network for optimization and image processing is presented. The hardware annealing function is also embedded in the network. It is a paralleled version of fast mean-field annealing in analog networks, and is highly efficient in finding globally optimal solutions for cellular neural networks. The network was designed to perform programmable functions for fine-grained processing with annealing control to enhance the output quality. A 5/spl times/5 prototype chip was fabricated in a 2.0 /spl mu/m CMOS technology. Since the MOSIS scalable design rules are used, it is also suitable for submicron technologies. For high circuit reliability and compactness purpose, a unit current of 6.0 /spl mu/A is used. The cell density is 505 cell/cm/sup 2/ and the cell time constant is chosen to be 0.3 /spl mu/s. From this prototype, a scalable VLSI core of around 50/spl times/50 neural processors can be integrated on a 1-cm/sup 2/ silicon area in a 0.8 /spl mu/m technology. Experimental results of building blocks and the prototype chip are also presented.

Optimal solutions for cellular neural networks by paralleled hardware annealing

An engineering annealing method for optimal solutions of cellular neural networks is presented. Cellular neural networks are very promising in solving many scientific problems in image processing, pattern recognition, and optimization by the use of stored program with predetermined templates. Hardware annealing, which is a paralleled version of mean-field annealing in analog networks, is a highly efficient method of finding optimal solutions of cellular neural networks. It does not require any stochastic procedure and henceforth can be very fast. The generalized energy function of the network is first increased by reducing the voltage gain of each neuron. Then, the hardware annealing searches for the globally minimum energy state by continuously increasing the gain of neurons. The process of global optimization by the proposed annealing can be described by the eigenvalue problems in the time-varying dynamic system. In typical nonoptimization problems, it also provides enough stimulation to frozen neurons caused by ill-conditioned initial states.