Pattern recognition by selforganizing neural networks. We discussed the bifurcation of a twoneuron cohen grossberg neural network with discrete delays in. As a model for competitive neural networks, the cohen grossberg neural network includes the lotkavolterra system, which is widely used for describing the dynamics of interacting populations see, e. Stability and hopf bifurcation of a delayed cohengrossberg. An introduction to computing with neural nets computing science.
Jan 04, 2014 cohengrossberg neural networks model is one of the most popular and typical neural network models. Note that a brief overview of randomness in neural networks and some. Stephen grossberg born december 31, 1939 is a cognitive scientist, theoretical and computational psychologist, neuroscientist, mathematician, biomedical engineer, and neuromorphic technologist. These neural networks have always included known brain mechanisms. Stephen grossberg, frank guenther, t daniel bullock, and douglas greve t boston university received 21 january 1992. Snipe1 is a welldocumented java library that implements a framework for. The function of the entire neural network is simply the computation of the.
Cohen and grossberg 3 proposed and studied an arti. Pdf global stability analysis for a class of cohengrossberg. Stability analysis of cohengrossberg neural networks with. Ann acquires a large collection of units that are interconnected. Preprocessing, in which converts the data and cluster the categories. In section 4, an illustrative example is given to show the effectiveness of the proposed theory. Nov 26, 2014 introduction the stabilityplasticity dilemma and rapid learning throughout life. Exponential synchronization of memristive cohengrossberg. The functional interpretation of these mechanisms has, however, often been novel because of the light thrown upon them by the behavioral analysis. New delaydependent stability criteria for cohengrossberg. Testing phase, which tests art1 network and check the performance.
Pdf stability analysis of cohengrossberg neural networks. Neural networks and natural intelligence by grossberg, stephen, 1939publication date 1988 topics neural networks computer science, neural computers, artificial intelligence, intellect publisher cambridge, mass. The cohengrossberg neural network model, proposed by cohen and grossberg in 1983, has been attracting much attention because of its wide application in various engineering fields and because of it being highly inclusive of other neural networks such as hopfield neural network, cellular neural network, recurrent neural network, and so on. Up to now, to the best of the authors knowledge, bifurcation of hop. The cohen grossberg neural network models, rst proposed and studied by cohen and grossberg 4, have been the subject of an active research due to their large application in various engineering and scienti c areas such as neural biology, population biology, and computing technology.
More recent work has led to the development of three classes of art neural network architectures. A spatial mapping neural network for object recognition and image understanding. Grossberg plenary ijcnn07 20 years of neural networks. Some other models, such as hopfield neural networks, cellular neural networks, and bidirectional associative memory neural networks, are special cases of the model kamel and xia 2009. The networks have also typically predicted the existence of unknown neural. In this paper, a delayed cohengrossberg neural network with diffusion under homogeneous neumann boundary conditions is investigated. Sep 22, 20 this paper investigates the globally asymptotical stability problem for a general class of cohen grossberg neural networks with multiple mixed timedelays. It is a self organizing, competitive network based on continuous time. The neural network in 4 can be described by the following system. Grossberg has been tremendously influential in engineering, dynamical systems, and. Sufficient conditions for the existence of local hopf bifurcation are obtained by analyzing the distribution of roots of characteristic equation. Dec, 20 another source of continuousnonlinear rnns arose through a study of adaptive behavior in real time, which led to the derivation of neural networks that form the foundation of most current biological neural network research grossberg, 1967, 1968b, 1968c. Since, stability analysis of cohengrossberg neural networks involving multiple time delays and multiple neutral delays is a difficult problem to overcome, the investigations of the stability conditions of the neutraltype the stability analysis of this class of neural network models have not been given much attention. We establish new criteria for the coexistence of equilibrium points and estimate their attracting domains.
Artificial neural network basic concepts tutorialspoint. As an important neural network model, the cohengrossberg neural network is very general and includes several wellknown neural networks, such as hopfield neural networks, cellular neural networks, recurrent neural networks and bidirectional associative memory networks with or without delays. Adaptive resonance theory, or art, is a cognitive and neural theory of how the brain autonomously learns to attend, categorize, recognize, and predict objects and events in a changing world. Among them, the cohengrossberg neural network cgnn, which was first proposed by cohengrossberg, is the most representative one since it comprises many popular neural networks as its special cases, such as hopfield neural networks and cellular neural networks. Xu, stability and bifurcation of a cohengrossberg neural network with discrete delays, appl. Sufficient conditions for the existence of local hopf bifurcation are obtained by analyzing the distribution of. Pdf periodic oscillations and bifurcation analysis for a. Harmless delays in cohengrossberg neural networks request pdf.
Stability in cohen grossbergtype bidirectional associative. Training phase, in which trains art1 neural network. Leading neural network proponents, like stephen grossberg and. In this paper, the global exponential robust stability is investigated for a class of reactiondiffusion cohengrossberg neural network with delays, this neural network contains time invariant. Bifurcation of a cohengrossberg neural network with discrete.
Neural dynamics of 1d and 2d brightness perception. This paper is concerned with pth moment exponential stability of stochastic cohengrossberg neural networks scgnn with timevarying connection matrix and delays. Stability analysis of inertial cohengrossberg neural networks with markovian jumping parameters. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed cohen grossberg neural. An adaptive resonance algorithm category learning and. Computer simulation of neural networks for perceptual psychology. Analysis of exponential stability for neutral stochastic. Before proving the main theorem, a more generalized convex combination inequality is proposed. Grossberg, a neuroscientist and a biomedical engineer, designed this network based on the human visual system shunting model. Stephen grossberg wang professor of cognitive and neural. New criteria for global stability of neutraltype cohen. Moreover, the direction and stability of hopf bifurcation are obtained by applying the normal form theory and the center manifold theorem.
Multiple stability and instability of cohengrossberg neural. Artificial neural network ann is an efficient computing system whose central theme is borrowed from the analogy of biological neural networks. Neural representations for sensorymotor control, ii. Bart kosko, have argued that neural networks di er from artificial intelligence. Compared with recurrent neural networks, hopfield neural networks, and cellular neural networks, it is more challenging and interesting to build cohen grossberg neural networks. Grossberg neural network with stochastic perturbations is introduced as follows. Work on artificial neural net models has a long history. Our results are not only presented in terms of system parameters. Function projective synchronization of memristorbased cohen. By analyzing the corresponding characteristic equation, the local stability of the trivial uniform steady state and the existence of hopf bifurcation at the trivial steady state are established, respectively. Cohen grossberg neural networks model was first introduced by cohen and grossberg in 1983, which has become one of the most important neural network models see 6, 7. Exponential stability of periodic solutions for inertial. Intrusion detection system based on carpentergrossberg.
Mar 16, 2010 the asymptotical meansquare stability analysis problem is considered for a class of cohen grossberg neural networks cgnns with random delay. A celebration special issue in honor of stephen grossbergs. Research article stability and hopf bifurcation of an n. Stability and hopf bifurcation of an nneuron cohengrossberg. Harmless delays in cohengrossberg neural networks request. Grossberg layer adjusts weights to obtain acceptable. Towards building a neural networks community, december, 2010 interviews. It is noted that cgnn is a very general class of neural network model, including a lot of. Intrusion detection system based on carpentergrossberg artificial. Periodic oscillations and bifurcation analysis for a cohengrossberg neural network model with impulsive perturbations. Hopf bifurcation in cohengrossberg neural network with. The circuit diagram and connection pattern implemented for the delayed bam neural networks can be found in 10. A cohen grossberg neural network with discrete delays is investigated in this paper. Asymptotic behavior of periodic cohengrossberg neural.
A new stability criterion for cohen grossberg neural networks with multiple timevarying delays is obtained by the employed general inequality. With the help of lyapunov function, stochastic analysis technique and the generalized halanay inequality, a set of novel sufficient conditions on pth moment exponential stability for scgnn is given. Pdf by constructing suitable lyapunov functionals and combining. Grossberg network is a artificial neural network introduced by stephen grossberg. Global stability of cohengrossberg neural network with both. A selforganizing neural network architecture for navigation using optic flow. Neural networks and natural intelligence mit cognet.
Since, stability analysis of cohen grossberg neural networks involving multiple time delays and multiple neutral delays is a difficult problem to overcome, the investigations of the stability conditions of the neutraltype the stability analysis of this class of neural network models have not been given much attention. Grossberg, a neuroscientist and a biomedical engineer, designed this network based on the human visual system. Stability analysis of inertial cohengrossberg neural. The evolution of the delay is modeled by a continuoustime homogeneous markov process with a finite number of states. Adaptive resonance theory art networks, as the name suggests, is always open to new learning adaptive without losing the old patterns resonance. Cerebellar and retinal analogs of cells fired by learnable or unlearned pattern classes. In this paper, we present multiplicity results of exponential stability and attracting domains for cohen grossberg neural network cgnn with distributed delays. Basically, art network is a vector classifier which accepts an input vector and classifies it into one of the categories depending upon which of the stored pattern it resembles the most. A cohengrossberg neural network with discrete delays is investigated in this paper.
The shunting model is one of grossberg s neural network models, based on a leaky integrator, described by the. In this paper, the global exponential robust stability is investigated for a class of reactiondiffusion cohen grossberg neural network with delays, this neural network contains time invariant. Estimate of multiple attracing domains for cohengrossberg. Stability switches in a cohengrossberg neural network with. Asymptotical mean square stability of cohengrossberg neural. The aim of this work is even if it could not beful. Anns are also named as artificial neural systems, or parallel distributed processing systems, or connectionist systems. Stability analysis of nonautonomous stochastic cohen. Yet the scientists who labored in the neural network field between the 1960s and 1980s were not widely known and. Periodic oscillations and bifurcation analysis for a cohen grossberg neural network model with impulsive perturbations.