Affiliations: University School of Basic & Applied Sciences, Nonlinear Dynamics Research Lab, Guru Gobind Singh Indraprastha University, Dwarka, Delhi, India
Abstract: This paper deals with the study of the co-existence of the chemical compounds CO2 and NO3 in substantial amounts over a long period of time for a wide range of atmospheric conditions. Using the presence of chemical compounds in the nature, the mathematical model for the behaviour is modelled. Lyapunov Characteristic Exponents (LCE) along with the indicators i.e., Small Alignment Index (SALI), Fast Lyapunov Indicator (FLI) and Dynamic Lyapunov Indicator (DLI) are applied to make a distinction concerning ordered/unordered trajectories of the dynamics for these chemical compounds. DLI indicator gives the largest of the eigenvalues of the Jacobian matrix and correct conclusions when applied to models of dynamical systems. FLI method is used to differentiate between regular motion and chaos in the intricate systems. SALI is a competent indicator of predictability which could discriminate amid different steady as well as randomness levels. FLI as well as SALI advance eigenvectors via iterating the progressing Jacobian matrix at every iteration for the set-up. Entropy, on the other hand, is the measure of randomness that would be generated as the system changes its state from consistency to chaos. It is observed that for stable environment the mutual sustenance of NO3 and CO2 should be maintained in a balanced manner, otherwise the environmental cycles get disrupted which results in rise in pollution levels.
Keywords: Fast Lyapunov Indicator-(FLI), Dynamic Lyapunov Indicator-(DLI), Small Alignment Index-(SALI), non-linear predictive model, Lyapunov Exponents, entropy
