Abstract
We propose a mathematical model for storage and recall of images using coupled maps. We start by theoretically investigating targeted synchronization in coupled map systems wherein only a desired (partial) subset of the maps is made to synchronize. A simple method is introduced to specify coupling coefficients such that targeted synchronization is ensured. The principle of this method is extended to storage/recall of images using coupled Rulkov maps. The process of adjusting coupling coefficients between Rulkov maps (often used to model neurons) for the purpose of storing a desired image mimics the process of adjusting synaptic strengths between neurons to store memories. Our method uses both synchronisation and synaptic weight modification, as the human brain is thought to do. The stored image can be recalled by providing an initial random pattern to the dynamical system. The storage and recall of the standard image of Lena is explicitly demonstrated.
Highlights
In this paper, we propose a mechanism for storage and recall of images that mimics the mechanisms used in the human brain
The resulting form of e2 is taken to be (0, 10, 42, 0, 10, −103, 10, 0, 31)T. Substituting this eigenvector in Eq (7) and following the procedure discussed above, we obtain the coupling matrix G that encodes this pattern. Using this G in Eq (1) (with f(x) given by the logistic map), we find that the desired targeted synchronization is achieved within the sets of {1, 4, 8} with x(n) as the synchronized state
Just as the human brain is thought to store memories by changing the pattern of synaptic strengths between neurons, in our model, the image is stored by changing coupling strengths between Rulkov maps
Summary
We propose a mathematical model for storage and recall of images using coupled maps. We start by theoretically investigating targeted synchronization in coupled map systems wherein only a desired (partial) subset of the maps is made to synchronize. The process of adjusting coupling coefficients between Rulkov maps (often used to model neurons) for the purpose of storing a desired image mimics the process of adjusting synaptic strengths between neurons to store memories. Our method uses both synchronisation and synaptic weight modification, as the human brain is thought to do.
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