This paper presents polychronous oscillatory cellular neural networks, designed for solving graph coloring problems. We propose to apply the Potts model to the four-coloring problem, using a network of locally connected oscillators under superharmonic injection locking. Based on our mapping of the Potts model to injection-locked oscillators, we utilize oscillators under divide-by-4 injection locking. Four possible states per oscillator are encoded in a polychronous fashion, where the steady state oscillator phases are analogous to the time-locked neuronal firing patterns of polychronous neurons. We apply impulse sensitivity function (ISF) theory to model and optimize the high-order injection locking of the oscillators. CMOS circuit design of a polychronous oscillatory neural network is presented, and coloring of a geographic map is demonstrated, with simulation results and design guidelines. There is good agreement between theory and Spectre simulation.

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用于解决图形着色问题的多时振荡细胞神经网络

本文介绍了多时振荡细胞神经网络，旨在解决图形着色问题。我们建议将 Potts 模型应用于四色问题，使用超谐波注入锁定下的本地连接振荡器网络。基于我们将 Potts 模型映射到注入锁定振荡器，我们利用 4 分频注入锁定振荡器。每个振荡器的四种可能状态以多时方式编码，其中稳态振荡器相位类似于多时神经元的时间锁定神经元放电模式。我们应用脉冲灵敏度函数 (ISF) 理论来建模和优化振荡器的高阶注入锁定。介绍了多同步振荡神经网络的 CMOS 电路设计，并演示了地理地图的着色，与仿真结果和设计指南。理论和 Spectre 模拟之间有很好的一致性。