Research Projects

In this study, we focus on designing simple memristor-based chaotic circuits and analyzing their dynamics using analytical, numerical, and experimental investigations. We aim to investigate the dynamical properties of these simple chaotic circuits and systems when subjected to external stimuli. One of the advantages of nonautonomous circuits is the control we have over their dynamics by varying the external force. This feature is straightforward to implement and can be demonstrated using electronic circuits, making it particularly appealing. The periodically induced circuits including memristor circuits could exhibit a rich variety of dynamical phenomena including chaotic hysteresis that exists over certain regions of the DC offset voltage about a chaotic attractor state. This designed memristor circuit can be extended for studying different types of chaos synchronization in coupled circuits without time delay. It is very interesting to note that there are only a few reported studies where different kinds of synchronization (mixed chaotic synchronization) in systems without time delay is observed. We design a time-delay electronic circuit and also memristor based time-delay circuit with simple nonlinearity, namely threshold nonlinearity and study their dynamics by numerical, experimental, and appropriate analytical techniques. This method is simple to construct using electronic circuits. In connection with this observation, the time delay circuit can be studied for the existence of chaotic hysteresis. The phenomenon of chaotic hysteresis that exists over certain regions of the DC offset parameter about a chaotic attractor state observed experimentally is validated through numerical simulation and explicit analytical solution studies. Complex networks have a very wide range of applications. In the present project, we apply our results to time-delay coupled circuits. Analysis of synchronization in the coupled time-delay circuits for chaos based computation and to propose an alternate scheme to implement dynamic logic gates for dynamic general-purpose computational hardware implementation. In this study, we explore how delay-coupled nonlinear circuits can be utilized to create dynamical logic gates. While these circuits exhibit dynamical logic gate behavior in the absence of coupling and delay, we consider the effects of coupling delay on the systems. By varying the delay for a certain range of coupling values, we can control the initial chaotic logic function of both systems to be the same logic function or change it to another logic function for both systems. Ultimately, the control parameter (delay) can be varied to achieve any desired logic function for the controlled dynamical logic gate. Further, we will extend our studies to the network of coupled circuits. In doing so we will compare our results with the all-to-all coupled models to gain a better understanding of complex networks.