Chapter Sexteen: Maps serving as the combined coupling between interacting environmental interfaces and their behavior in the presence of dynamical noise
Many physical and biological problems, in addition to environmental problems, can be described by the dynamics of driven coupled oscillators. To study their behavior as a function of coupling strength and nonlinearity, we considered the dynamics of two maps acting as the combined coupling (diffusive and linear) in the above fields. First, we considered a logistic difference equation on an extended domain that is a part of the maps, and we discuss it using its bifurcation diagram, Lyapunov exponent, sample and permutation entropy. Second, we performed the dynamical analysis of the coupled maps using Lyapunov exponents and crosssample entropy for the dependence of two coupling parameters. Further, we investigated how dynamic noise can affect the structure of these bifurcation diagrams. This investigation was performed with noise entering in two specific ways, which disturbs either the logistic parameter on the extended domain or places an additive “shock” to the state variables. Finally, we demonstrated the effect of forcing by parametric noise on the Lyapunov exponent of coupled maps.