ABSTRACT
Several systems of geomorphological interest undergo morphological changes with time. In the process of changing morphological organization, systems traverse various phases. It is understood through numerous studies that the geomorphological systems undergo nonlinear processes. One equation that explains several phases that a system could undergo is logistic equation, which is also termed as first-order nonlinear difference equation. In this equation, important parameters include the strength of the nonlinearity parameter that controls the dynamics of a system and the state of the systems (e.g., initial condition). Logistic equation is based on a wonderful recipe to simulate the processes in such a way that when the system attains a higher value (e.g., population of a specie, fractal dimension, area of a lake), this equation reduces this to a lower value in the next time step, and vice versa. Using the values obtained via the iteration of the logistic equation, by changing the strength of control parameters, several spatiotemporal dynamics that we studied under strong theoretical assumptions include behaviors of (1) water bodies under controlled stream flow discharges, (2) highly ductile fold dynamics, and (3) pyramidal sand dune dynamics and avalanche size distributions.
