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