Browsing by Author "Bakrani, Sajjad"

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Citation - WoS: 1
Citation - Scopus: 0
Cycle-Star Motifs: Network Response To Link Modifications
(Springer, 2024) Bakrani, Sajjad; Eroğlu, Deniz; Kiran, Narcicegi; Eroglu, Deniz; Pereira, Tiago
Understanding efficient modifications to improve network functionality is a fundamental problem of scientific and industrial interest. We study the response of network dynamics against link modifications on a weakly connected directed graph consisting of two strongly connected components: an undirected star and an undirected cycle. We assume that there are directed edges starting from the cycle and ending at the star (master-slave formalism). We modify the graph by adding directed edges of arbitrarily large weights starting from the star and ending at the cycle (opposite direction of the cutset). We provide criteria (based on the sizes of the star and cycle, the coupling structure, and the weights of cutset and modification edges) that determine how the modification affects the spectral gap of the Laplacian matrix. We apply our approach to understand the modifications that either enhance or hinder synchronization in networks of chaotic Lorenz systems as well as R & ouml;ssler. Our results show that the hindrance of collective dynamics due to link additions is not atypical as previously anticipated by modification analysis and thus allows for better control of collective properties.
Citation - WoS: 0
Citation - Scopus: 0
Invariant Manifolds of Homoclinic Orbits and the Dynamical Consequences of a Super-Homoclinic: a Case Study in R4 With Z2-Symmetry and Integral of Motion
(Academic Press Inc Elsevier Science, 2022) Bakrani, Sajjad; Lamb, Jeroen S. W.; Turaev, Dmitry
We consider a Z(2)-equivariant flow in R-4 with an integral of motion and a hyperbolic equilibrium with a transverse homoclinic orbit Gamma. We provide criteria for the existence of stable and unstable invariant manifolds of Gamma. We prove that if these manifolds intersect transversely, creating a so-called super-homoclinic, then in any neighborhood of this super-homoclinic there exist infinitely many multi-pulse homoclinic loops. An application to a system of coupled nonlinear Schrodinger equations is considered. (C) 2022 The Authors. Published by Elsevier Inc.