The analysis of stability and stabilization in dynamical systems, spanning fields such as physical, biological, and engineering, allows for the exploration of complex phenomena. This includes delving into the intricate dynamics of prey and predator relationships, incorporating Allee effects induced by factors like the cost of predation fear and their subsequent impacts. Additionally, nonlinear dynamics serves as a valuable tool to investigate emergent behaviors within these complex systems, shedding light on the intricate interactions and dynamics that underpin them. This interdisciplinary approach fosters a deeper understanding of the complex relationships and behaviors that manifest in natural and engineered systems, enhancing our ability to predict and manipulate their outcomes.

Vision

• Analyze the stability and stabilization of dynamical systems, which arise from the disciplines such as physical, biological, and engineering.
• Exploring the prey-predator dynamics by modelling the Allee effects induced by cost of predation fear and its carry-over effects.

Mission

• To analyze the stability and stabilization of dynamical systems.
• To study the emergent behaviour in a Complex system using nonlinear dynamics as a tool.
• Exploring the prey-predator dynamics by modelling the Allee effects induced by cost of predation fear and its carry-over effects.

Proposed initiative

• Formulate a mathematical model for the transmission dynamics of the disease    COVID19 and study its stability.
• Formulating a mathematical model to understand the proliferation of COVID19 using in-host dynamical model and formulating mathematical model for the disease cancer. 
• Study the fractional model of differential system with different controllers. 
• Study the dynamics of network of coupled oscillators with higher order interactions.
• Explore the existence of different spatial patterns in e-epidemiological and ecological model generated by self and cross-diffusion