Multidirectional Associative Memory Neural Networks Research Articles

Existence, uniqueness and global exponential stability of a periodic solution for a class of multidirectional associative memory neural network models

A multidirectional associative memory (MAM) neural network with periodic coefficients and distributed delays is studied. By constructing a Poincare mapping, some sufficient conditions are obtained ensuring existence, uniqueness and the global exponential stability of a periodic solution of MAM neural network. The result is new to MAM neural networks. An example is given to illustrate the effectiveness of the result.

Almost periodic solution for multidirectional associative memory neural network with distributed delays

This paper proposes a mathematical model of multidirectional associative memory (MAM) neural network with almost periodic coefficients and continuously distributed delays. By using exponential dichotomy and spectral radius, a sufficient condition for the existence and the global exponential stability of an almost periodic solution is obtained. Two examples are given to illustrate the effectiveness of our results.

Multistability in a Multidirectional Associative Memory Neural Network with Delays

This paper focuses on the multidirectional associative memory (MAM) neural networks with <i >m</i> fields which is more advanced to realize associative memory. Based on the Brouwer fixed point theorem and Dini upper right derivative, it is confirmed that the multidirectional associative memory neural network can have <svg style="vertical-align:-0.1638pt;width:12.1125px;" id="M1" height="16.9625" version="1.1" viewBox="0 0 12.1125 16.9625" width="12.1125" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,16.7)"><path id="x33" d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5&#xA;q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" /></g> <g transform="matrix(.012,-0,0,-.012,8.225,8.537)"><path id="x1D459" d="M238 681l-124 -585q-7 -31 4 -31q10 0 37.5 18.5t49.5 41.5l16 -22q-40 -48 -89.5 -81.5t-76.5 -33.5q-42 0 -16 122l105 488q7 32 0 41t-39 9h-35l5 26q35 3 71 13t58 17.5t26 7.5q14 0 8 -31z" /></g> </svg> equilibria and <svg style="vertical-align:-0.0pt;width:12.1125px;" id="M2" height="16.75" version="1.1" viewBox="0 0 12.1125 16.75" width="12.1125" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,16.7)"><path id="x32" d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" /></g> <g transform="matrix(.012,-0,0,-.012,8.225,8.538)"><use xlink:href="#x1D459"/></g> </svg> equilibria of them are stable, where <i >l</i> is a parameter associated with the number of neurons. Furthermore, an example is given to illustrate the effectiveness of the results.

Global Exponential Stability of Discrete-Time Multidirectional Associative Memory Neural Network with Variable Delays

A discrete-time multidirectional associative memory neural networks model with varying time delays is formulated by employing the semidiscretization method. A sufficient condition for the existence of an equilibrium point is given. By calculating difference and using inequality technique, a sufficient condition for the global exponential stability of the equilibrium point is obtained. The results are helpful to design global exponentially stable multidirectional associative memory neural networks. An example is given to illustrate the effectiveness of the results.

Existence and Exponential Stability of Multiple Periodic Solutions for a Multidirectional Associative Memory Neural Network

The paper proposes several mathematical models of the multidirectional associative memory (MAM) neural network by analyzing its structure. A model of MAM with distributed delays is studied. Under some new assumptions on activation functions, $${2^{n_0[m/2]}}$$ invariant subsets of MAM are constructed. Then the existence and the exponential stability of $${2^{n_0[m/2]}}$$ periodic solutions located on invariant subsets are obtained by constructing a suitable Liapunov function and a Poincare mapping. An estimating method of the exponential convergence rate is given. The obtained results are new to MAM neural networks. An example is given to illustrate the effectiveness of the results.