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Small-world and scale-free networks are known to be more easily synchronized than regular lattices, which is usually attributed to the smaller network distance between oscillators. Surprisingly, we find that networks with a homogeneous distribution of connectivity are more synchronizable than heterogeneous ones, even though the average network distance is larger. We present numerical computations and analytical estimates on synchronizability of the network in terms of its heterogeneity parameters. Our results suggest that some degree of homogeneity is expected in naturally evolved structures, such as neural networks, where synchronizability is desirable.

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Our study of thalamo-cortical systems suggests a new architecture for a neurocomputer that consists of oscillators having different frequencies and that are connected weakly via a common medium forced by an external input. Even though such oscillators are all interconnected homogeneously, the external input imposes a dynamic connectivity. We use Kuramoto's model to illustrate the idea and to prove that such a neurocomputer has oscillatory associative properties. Then we discuss a general case. The advantage of such a neurocomputer is that it can be built using voltage controlled oscillators, optical oscillators, lasers, microelectromechanical systems, Josephson junctions, macromolecules, or oscillators of other kinds. (Provisional patent 60͞108,353) [S0031-9007(99)08813-4] PACS numbers: 87.10. + e, 05.45. -a, 07.05.Mh, 42.79.TaIt is believed that a new generation of computers will employ principles of the human brain. Such a computer, often referred to as a neurocomputer, consists of many interconnected units (referred to here as neurons) performing simple nonlinear transformations in parallel. Unlike a von Neumann computer, the neurocomputer does not execute a list of commands (a program). Its major aim is not a general-purpose computation, but pattern recognition via associative memory. There are many neural network models that can be used as a theoretical basis for a neurocomputer; see [1] for comprehensive review. The most promising are oscillatory neural networks because they take into account rhythmic behavior of the brain [2-7].Whether oscillatory or not, a neurocomputer consisting of n neurons needs n 2 programmable connections (see Fig. 2), so building such a computer is a major challenge when n is large. A possible way to cope with this problem was suggested by our study of thalamo-cortical systems [8][9][10]. We treat the cortex as being a network of weakly connected autonomous oscillators forced by the thalamic input; see Fig. 1. We find that whether or not such oscillators communicate depends on their frequencies: If two oscillators have nearly equal frequencies, then they do communicate in the sense that the phase (timing) of one of them is sensitive to the phase of the other.In contrast, when they have essentially different frequencies, their phases uncouple. Thus, an oscillator can interact selectively with other oscillators having appropriate frequencies. In analogy with radio, we refer to such interactions as being frequency modulated (FM).We also find that a weak thalamic input having appropriate frequencies in its power spectrum can dynamically connect any two oscillators, even those that have different frequencies and would be unlinked otherwise.This suggests the following design of a neurocomputer: It consists of oscillators having different frequencies and connected homogeneously and weakly to a common medium (see Fig. 2). Selective communication between such oscillators can be created by the weak forcing. We illustrate some major points using Kuramoto's model in the section below, and we d...

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Abstract-We propose a novel architecture of an oscillatory neural network that consists of phase-locked loop (PLL) circuits. It stores and retrieves complex oscillatory patterns as synchronized states with appropriate phase relations between neurons.Index Terms-Brain rhythms, oscillatory associative memory, temporal pattern recognition, voltage-controlled oscillators (VCO's).

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