• Sachin Bhalekar

Articles written in Pramana – Journal of Physics

• Dynamics of fractional-ordered Chen system with delay

In the present paper the effect of delay on chaos in fractional-order Chen system is investigated. It is observed that inclusion of delay changes chaotic behaviour to limit cycles or stable systems.

• Analysing the stability of a delay differential equation involving two delays

Analysis of systems involving delay is a popular topic among the applied scientists. In the present work, we analyse the generalised equation $D^{\alpha}x(t) = g(x(t − \tau_{1}), x(t − \tau_{2}))$ involving two delays, viz. $\tau_{1} \geq 0$ and $\tau_{2} \geq 0$. We use stability conditions to propose the critical values of delays.Using examples,we show that the chaotic oscillations are observed in the unstable region only. We also propose a numerical scheme to solve such equations.

• Analysis of solution trajectories of fractional-order systems

The behavior of solution trajectories usually changes if we replace the classical derivative in a system with a fractional one. In this article, we throw light on the relation between two trajectories $X (t)$ and $Y (t)$ of such a system, where the initial point $Y$ (0) is at some point X (t1) of the trajectory $X (t)$. In contrast with classical systems, these trajectories $X$ and $Y$ do not follow the same path. Further, we provide a Frenet apparatus for both trajectories in various cases and discuss their effect.

• # Pramana – Journal of Physics

Volume 96, 2022
All articles
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Posted on July 25, 2019

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