Irina Surina

Tunable Oscillatory Network for Visual Image Segmentation

Recurrent oscillatory network with tunable oscillator dynamics and nonlocal dynamical interaction has been designed. Two versions of the network model have been suggested: 3D oscillatory network of columnar architecture that reflects some image processing features inherent in the brain visual cortex, and 2D version of the model, obtained from the 3D network by proper reduction. The developed image segmentation algorithm is based on cluster synchronization of the reduced network that is controlled by means of interaction adaptation method. Our approach provides successive separation of synchronized clusters and final decomposition of the network into a set of mutually desynchronized clusters corresponding to image fragments with different levels of brightness. The algorithm demonstrates the ability of automatic gray-level image segmentation with accurate edge detection. It also demonstrates noise reduction ability.

Macrodynamic approach for oscillatory networks

The system of coupled oscillators, interacting via arbitrary symmetric matrix of connections, is studied from a viewpoint of associative memory modelling. A self-consistent field approach which consists in operating with a finite number of macrovariables (appropriate inner products which can be regarded as order parameters) is used. A system of dynamic equations of oscillatory network being rewritten in terms of macrovariables has a form of independent equations. Being completed by functional equations for order parameters, this system provides a self-consistent description of the oscillatory network. In particular, the approach can be used as an instrument for studying the dependence of the number of network phase locked states on the frequency distribution and the architecture of connections. The abilities of this approach are demonstrated in the case of a network with all-to-all uniform connections.

Oscillatory Networks with Hebbian Matrix of Connections

The systems of symmetrically coupled limit cycle oscillators admit the design of recurrent associative memory networks with Hebbian matrix of connections. Unlike the similar neural networks this matrix proved to be the complex-valued Hermitian one with nonzero diagonal. In the case of strong interaction in oscillatory system the memory vectors of the network are slightly perturbed properly normalized eigenvectors of matrix of connections. They can be calculated by perturbation method on the appropriate small parameter. The self-consistent analysis of dynamical system fixed points in the case of homogeneously all-to-all connected oscillators is presented. It is proved that for positive values of connection strength only a single memory vector can be stored. Some questions concerning the ”extraneous” memory of the networks are discussed.

Recurrent Associative Memory Network of Nonlinear Coupled Oscillators

The recurrent associative memory networks with complex-valued Hebbian matrices of connections are designed from interacting limit-cycle oscillators. These oscillatory networks have peculiarities and advantages as compared to Hoplield neural network model. In particular, the class of networks with high memory characteristics (the capacity close to 1, low extraneous memory) exists. At zero values of oscillator frequencies the designed networks are closely related to the known “clock” neural networks (networks from complex-valued neurons). Pattern recognition of colored images and recognition of objects with complicated topological structure look quite natural in the context of such models. Exact solutions have been obtained for a few types of the networks considered, in particular, for homogeneous closes chains.

Exact solutions and modeling of associative memory in oscillatory networks

This paper is devoted to the study of associative memory in the networks of N coupled nonlinear oscillators interacting via complex-valued weights. Exact solutions relating to the structure of attractors have been obtained. The complete solution to the systems of two oscillators and the structural portrait of the governing dynamical system have been obtained. It is shown that homogeneous closed chains of oscillators play important role in the context of phase associative memory problems. Qualitative description of the memory in the closed chains of N oscillators is given for arbitrary N, and rigorous solutions for N <EQ 6 are illustrated. The networks considered admit electronic, nonlinear optical and optoelectronic implementations. The background of some of them is under development.

Pattern Formation in Locally Connected Oscillatory Networks

The subject of our study is a class of networks consisting of locally connected nonlinear oscillators. In spatially continual limit these oscillatory networks can be considered as oscillatory media governed by a system of reaction-diffusion equations. Formation of spatio-temporal patterns in nonlinear active media (wave trains, standing waves, targets and shock structures, spiral waves, stripe patterns, cluster states ) is the subject of interest in physical, chemical, biological problems.

Oscillatory network model of the brain visual cortex with controlled synchronization

Oscillatory network for modelling of synchronization-based functioning of the brain visual cortex is presented. Single network oscillator, imitating the behavior of simple cells of the visual cortex, demonstrates stimulus-dependent intrinsic dynamics-stable oscillations or quick relaxation. Three-dimensional spatial architecture of the network simulates the columnar structure of the visual cortex. Nonlinear nonlocal dynamical interaction of oscillators depends on instantaneous oscillator activities and orientations of receptive fields. Two-dimensional averaged network of idealized oscillator-columns is extracted. The model demonstrates controlled synchronization of image-dependent clusters of oscillatory network and self-controlled suppression of noisy background.

Pattern formation in active oscillatory media and its relation to associative memory networks

We continue to study the arrays of nonlinear coupled oscillators. The networks of associative memory based on limit-cycle oscillators connected via complex-valued Hermnian matrices were previously designed. Another class of networks consisting of locally connected nonlinear oscillators, closely related to so-called cellular neural networks, is the subject of study in the present paper. Within spatially continual limitations, these oscillatory networks can be considered as oscillatory media governed by the system of reaction-diffusion equations. Formation of spatio-temporal dissipative structures (wave trains, standing waves, targets and shock structures, spiral waves, stripe patterns, cluster states) in various nonlinear active media is widely used for modeling of complicated nonlinear phenomena in physics, chemistry, biology, neurophysiology. Here the results of analytical study of 1D oscillatory media corresponding to closed and unclosed chains of limit-cycle oscillators are presented. Conditions of existence of some spatio-temporal regimes inherent to nonlinear active media (diffusion instability caused by coupling, formation of wave trains and standing waves) have been clarified.

Phase Memory in Oscillatory Networks

As it was shown earlier, oscillatory networks consisting of limit-cycle oscillators interacting via complex-valued connections can be used for associative memory design. Phase memory as a special type of associative memory in oscillatory networks has been invented and studied. Detailed analysis of phase memory features of phasor networks related to oscillatory networks has been performed. It has been found that under special choice of parameters the oscillatory networks possess high memory storage capacity and low extraneous memory.

Modeling of associative memory in systems of phase oscillators

For the model of coupled phase oscillators, problems of associative memory are considered. It is demonstrated that the networks of oscillators possess some necessary properties for associative memory design. In the case of networks with a tree-like structure of connections, only one pattern can be placed at any prescribed point in the phase space. An approach to the analysis of the number and possible locations of memory images is suggested. It is based on the fact of the existence of invariant sets of critical points.