Research Interests in Brief

This work focuses on the stability analysis of nonlinear dynamical systems that admit multiple equilibrium points. Such systems commonly arise in engineering and applied sciences, where different initial conditions may lead to different long-term behaviors. The main objective is to develop analytical conditions for characterizing stability, convergence, and basin-of-attraction properties in the presence of multiple stable and unstable equilibria. These ideas have applications in control systems, power electronics, synchronization problems, epidemic models, and other nonlinear systems where multistability plays an important role.

This work focuses on the synchronization of chaotic and hyperchaotic systems, where two or more complex nonlinear systems are driven to exhibit coordinated behavior despite their sensitive dependence on initial conditions. The main objective is to design suitable control strategies that ensure synchronization between master and slave systems, including reduced-order synchronization and synchronization under time-delay effects. These concepts have applications in secure communication, signal processing, nonlinear control, biological systems, and engineering systems where complex dynamic behavior must be regulated or coordinated.

My interest in applied mathematics lies in using rigorous mathematical tools to analyze real-world problems arising in engineering, science, and technology. This includes the study of differential equations, dynamical systems, stability theory, optimization, matrix analysis, matrix measure theory, exterior algebra, additive compound matrices, and control-theoretic methods. These tools provide a strong mathematical foundation for understanding stability, convergence, synchronization, contraction, and transient behavior in nonlinear and complex engineering systems. The main objective is to develop mathematically sound and practically useful frameworks for analyzing and controlling dynamical systems.

This work focuses on master-slave synchronization using RF communication, where the dynamics of a master system are transmitted wirelessly to a slave system to achieve coordinated behavior. The main objective is to design and implement a reliable synchronization strategy under practical communication constraints such as signal delay, noise, bandwidth limitation, and data loss. Such a framework is useful for studying real-time synchronization of nonlinear systems, secure communication, wireless control, remote monitoring, and communication-based coordination of engineering systems.