A new Network Simulation Method for the characterization of delay differential equations

Abstract

In this work, we provide for the first time the characterization of delay terms in systems of delay differential equations within the frame of the Network Simulation Method, a procedure that sets a formal equivalence between the system of differential equations and an electrical network. The results were not achieved previously, which strengths the formalism of the model and provides new opportunities for the method. Free circuit software LTspice is employed to conduct the simulations, which requires few simulation rules and can be programmed either by electrical symbol code or text file. Very few devices are needed to design the network model, and the delay terms are easily implemented by voltage-controlled voltage sources. A practical example for delayed adsorption/desorption kinetics is employed to test the methodology, being the results compared with software Mathematica. Additionally, the modelling of pulse width in passively mode-locked quantum dot lasers by the application of a reverse bias voltage is addressed, which constitutes a promising application in communications and advanced sensing. The power, versatility and simplicity of the Network Simulation Method enables it as an exceptional alternative to solve complex systems described by delay differential equations, from both researching and educational points of view.

Keywords

• Electrical analogy
• Network Simulation Method
• Numerical simulations
• Delay differential equations
• Electrical circuits