An Investigation on Synchronized Cycles of Generalized Nicholson-Bailey Model

In this paper, we study a drive-response discrete-time dynamical system which has been coupled
using convex functions and we introduce a synchronization threshold which is crucial for the
synchronizing procedure. Chaos is a complex nonlinear phenomenon that has been increasingly
studied in the last three decades. During those years, many fields of science and engineering have
been affected by chaos studies. We provide one application of this type of coupling in synchronized
cycles of a generalized Nicholson-Bailey model. This model demonstrates a rich cascade of complex
dynamics from stable fixed point to periodic orbits, quasi periodic orbits and chaos. We explain how
this way of coupling makes these two chaotic systems starting from very different initial conditions,
quickly get synchronized. We investigate the qualitative behavior of GNB model and its synchronized
model using time series analysis and its long time dynamics by the help of bifurcation diagram. In
chaotic regime, for larger values of synchronization constant s, closer to one, we could not get a
complete synchronization. But, for smaller synchronization constant s, closer to zero, we have shown
that two systems are in complete synchronization when the dynamic is chaotic.