Maps serving the combined coupling for use in environmental models and their behaviour in the presence of dynamical noise

Abstract

Many physical, biological as well as the environmental problems, can be described by the dynamics of driven coupled oscillators. In order to study their behaviour as a function of coupling strength and nonlinearity, we considered dynamics of two maps serving the combined coupling (diffusive and linear) in the above fields. Firstly, we have considered a logistic difference equation on extended domain that is a part of the maps, that is discussed using its bifurcation diagram, Lyapunov exponent, sample as well as the permutation entropy. Secondly we have performed the dynamical analysis of the coupled maps using Lyapunov exponent and cross sample entropy in dependence on two coupling parameters. Further, we investigated how dynamical noise can affects the structure of their bifurcation diagrams. It was done (i) by the noise entering in two specific ways, that disturbs either the logistic parameter on extended domain or (ii) by an additive “shock” to the state variables. Finally, we demonstrated the effect of forcing by parametric noise, introduced in all maps’ parameter, on Lyapunov exponent of coupled maps.