Stability Analysis of Multi-Delay Differential Equations Using Aboodh Transform Method: Parkinson’s Disease Model

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In this study, we investigate the stability of multi - delay differential equations (MDDEs) associated with Parkinson’s disease model using the Aboodh integral transform method, which is a powerful way to make delay systems easier to understand. The Aboodh integral transform does a good job of dealing with delay terms by turning them into algebraic statements in the transform domain. This makes it easy to write the characteristic equation. We find the conditions under which different MDDEs are stable by looking at the roots of the characteristic equation. The suggested method has been tested in Aboodh integral transform, all of which have situations where multiple delays have a big effect on how the system works. The Parkinson’s disease model is asymptotic stability stable and will return to a steady state eventually after disturbances, and reverting to its initial condition. The Aboodh integral transform turns delay terms into exponential factors in the transform domain, which makes stability analysis easier by turning it into an algebraic root - finding problem that can be handled. The analytical models show that the method is more accurate and uses less computing power for systems with long delays or interactions between multiple delays.

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