One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or the parameters of the medium requires one to redo the simulations. This makes it difficult to design modulation schemes and practically impossible to prove the optimality of a given transmission strategy. In this paper, we provide an analytical technique for modeling the non-linearity of chemical reaction equations based on the perturbation method. The perturbation method expresses the solution in terms of an infinite power series. An approximate solution can be found by keeping the leading terms of the power series. The approximate solution is shown to track the true solution if either the simulation time interval or the reaction rate is sufficiently small. Approximate solutions for long time intervals are also discussed. An illustrative example is given. For this example, it is shown that when the reaction rate (or the total time interval) is low, instead of using a continuous release waveform, it is optimal for the transmitters to release molecules at two time instances.

翻译：扩散基分子通信的主要挑战之一是处理反扩散化学方程式的非线性。 虽然可以使用数字方法解决这些方程式, 但输入信号或介质参数的改变需要重新进行模拟。 这使得设计调制方案十分困难, 也几乎无法证明特定传输战略的最佳性。 在本文中, 我们提供了一个分析技术, 用于模拟基于扰动法的化学反应方程式的非线性。 扰动法用无限的能量序列表示解决办法。 一种近似的解决办法可以通过保留电源序列的主要条件找到。 如果模拟时间间隔或反应率都足够小, 则显示大致的解决办法可以追踪真正的解决办法。 也讨论了长时间间隔的近似解决办法。 举例来说, 当反应率( 或总时间间隔) 较低时, 而不是使用连续释放波形, 其对于发报器在两个时间段释放分子是最佳的。