Multistability Of Recurrent Neural Networks And Its Application In Associative Memory

As a complex mathematical calculation model capable of parallel information processing,artificial neural networks?ANNs?have been studied by many scholars in recent decades.Nowadays,neural networks have been widely applied to implement artificial intelligence,optimal control,pattern recognition,associative memory image processing,etc.As an application that imitates human memory,associative memory has a higher recognition rate with inputs which have large noises.Compared to other kinds of neural networks,recurrent neural networks?RNNs?can be better applied to associative memory and pattern recognition.Hence it is necessary to study the dynamic behaviors of recurrent neural networks.When applying recurrent neural network to associative memory,it is necessary to associate the pattern which needs to be remembered with the equilibrium points of the recurrent neural network.The number of equilibrium points of the neural network determines the memory capacity,therefore,the study of the multistability of recurrent neural networks has important theoretical and engineering significance.First,this paper introduces the research status and research background of artificial neural network,and then introduces the relevant research significance and research status for the multistability of recurrent neural networks.Through rigorous mathematical proof,the sufficient conditions for the recurrent neural network to have a certain number of equilibrium points,invariant sets and local stable equilibria are obtained.The simulation experiments are carried out by using MATLAB,and the related simulation associative memory applications are designedThe main contents of this paper are as follows:?1?This paper addresses memristive neural networks?MNNs?and its multistability.Through region partition method,for n-dimensional memristive RNNs with a class of general nonmonotonic activation functions,sufficient criteria are proposed for that network has?27?+3)⁹)equilibrium points,of which?7?+2)⁹)equilibrium points are locally exponentially stable.Compared with the existing similar work,the network has more equilibrium points,which provides a more reliable theoretical basis for the design of associative memory applications,and numerical examples are also given to verify the feasibility of the theory.?2?Through region partition method,for n-dimensional fractional-order recurrent neural networks?FORNNs?with a class of discontinuous activation functions,sufficient criteria are proposed to ensure that network has?26?+3)⁹)?6??1)equilibrium points,of which?7?+2)⁹)equilibrium points are locally Mittag-Leffler stable.Numerical examples are also given to verify the feasibility of the theory.?3?Firstly,for the MNNs with a class of general nonmonotonic activation functions,the corresponding hetero-associative memory application is designed.By setting some conditions,the weights of the network are calculated directly by the equations.Given a group of input with certain noises,the network can output the correct corresponding pattern,which verifies the feasibility of applying this kind of MNNs to associative memory;Then,a corresponding self-associative memory application is designed for fractional neural networks with a class of discontinuous activation functions.Given a group of input with certain noises,the network can output the correct corresponding pattern,which verifies the feasibility of applying this kind of FORNNs to associative memory.