Stability Analysis of Pantograph Delay Differential Equations
Provides theoretical stability analysis for a class of delay differential equations with proportional delay, relevant to mathematical analysis and modeling in applied sciences.
The paper derives analytic stability criteria for pantograph delay differential equations, partitioning the parameter plane into unstable, asymptotically stable, and delay-dependent stability regions, with numerical simulations confirming sharp boundaries.
This article investigates the stability of pantograph delay differential equations, in which the delayed argument is proportional to the present time. We derive analytic criteria that partition the parameter plane into unstable, asymptotically stable, and delay-dependent stability regions. The theoretical results are supported by numerical simulations that illustrate the sharpness of the stability boundaries. We also formulate a proportional-delay analogue of the Mackey--Glass chaotic delay differential equation and examine the resulting dynamical behaviour.