ANALYSIS OF CHAOS THEORY FOR NONLINEAR DYNAMICAL SYSTEMS

A dynamic model has been created to examine the ecological system, with a focus on how international trade affects ecological footprint and carrying capacity. The stability evaluation of the system has been carried out while taking into account the influence of different factors and maintaining other conditions constant. A chaotic attractor's unstable periodic orbits have also been successfully stabilised using the Constant Feedback Chaos Control technique. This control method's effectiveness has been proven through numerical simulations. Using this model, we have learned more about the intricate nonlinear connections between international trade, the environmental impact, and ecological capacity for carrying. The introduction of Chaos Theory as a potent framework for comprehending the behaviour of nonlinear dynamical systems marks the beginning of the abstract. It draws attention to the chaotic nature of complex systems, where slight variations in the original circumstances can eventually result in quite different results. This characteristic is frequently referred to as the "butterfly effect." The importance of Chaos Theory is emphasised in the abstract across a range of disciplines, including physics, biology, economics, and social sciences. It demonstrates how the use of Chaos Theory has yielded important insights into complicated processes that were previously challenging to understand using conventional linear methods.