Lyapunov exponent using Euler’s algorithm with applications in optimization problems

The difference and differential equations have played an eminent part in nonlinear dynamics systems, but in the last two decades one-dimensional difference maps are considered in the forefront of nonlinear systems and the optimization of transportation problems. In the nineteenth century, the nonlinear systems have paved a significant role in analyzing nonlinear phenomena using discrete and continuous time interval. Therefore, it is used in every branch of science such as physics, chemistry, biology, computer science, mathematics, neural networks, traffic control models, etc. This paper deals with the maximum Lyapunov exponent property of the nonlinear dynamical systems using Euler?s numerical algorithm. The presents experimental as well as numerical analysis using time-series diagrams and Lyapunov functional plots. Moreover, due to the strongest property of Lyapunov exponent in nonlinear system it may have some application in the optimization of transportation models.