In this research, we investigate synchronisation effects in a discrete-time dynamical system using homotopy and Lipschitz notions. By developing a novel link function with Lipschitz threshold, we have broadened the scope of the prior findings in this field. We constantly transform the orbits of the original model into the linked model using this new link function while maintaining qualitative characteristics like stability and periodicity. We demonstrate that for less than this threshold, two systems are entirely synchronised, i.e., they eventually evolve in time the same way. We arrive at this Lipschitz synchronisation threshold analytically. We use this approach to analyse a one-dimensional Ricker type population model, which is notorious for having chaotic trajectory. Utilizing methods from qualitative dynamical systems like the Poincare section, For various synchronisation Lipschitz thresholds (S) and growth rates, chaotic dynamics and chaotic signals are detected using spectrum and time series (r\). Finally, utilising mean phase and amplitude discrepancies, we quantitatively determine the Lipschitz synchronisation threshold for various growth rates.
Tahmineh Azizi,
Florida State University, USA.
Please see the link here: https://stm.bookpi.org/NRAMCS-V5/article/view/7486
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