We simulate a four-node fully connected phase-locked loop (PLL) network with an architecture similar to the neural network proposed by Hoppensteadt and Izhikevich (1999, 2000), using second-order PLLs. The idea is to complement their work analyzing some engineering questions like:how the individual gain of the nodes affects the synchronous state of whole network; how the individual gain of the nodes affects the acquisition time of the whole network; how close the free-running frequencies of the nodes need to be in order to the network be able to acquire the synchronous state; how the delays between nodes affect the synchronous state frequency. The computational results show that the Hoppensteadt-Izhikevich network is robust to the variation of these parameters and their effects are described through graphics showing the dependence of the synchronous state frequency and acquisition time with gains, free-running frequencies, and delays.

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We analytically investigate the existence of global and partial synchronism in neural networks where each node is represented by a phase oscillator. Partial synchronism, which is important to pattern recognition, can be caused by increasing the natural frequency of an oscillator and restricting the frequencies of others in certain ranges.

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