Abstract
We consider the coupling between two networks, each having N nodes whose individual dynamics is modeled by a two-state master equation. The intra-network interactions are all-to-all, whereas the inter-network interactions involve only a small percentage of the total number of nodes. We demonstrate that the dynamics of the mean field for a single network has an equivalent description in terms of a Langevin equation for a particle in a double-well potential. The coupling of two networks or equivalent coupling of two Langevin equations demonstrates synchronization or anti-synchronization between two systems, depending on the sign of the interaction. The anti-synchronized behavior is explained in terms of the potential function and the inter-network interaction. The relative entropy is used to establish that the conditions for maximum information transfer between the networks are consistent with the principle of complexity management and occurs when one system is near the critical state. The limitations of the Langevin modeling of the network coupling are also discussed.
Highlights
The significance of synchronization for the understanding of complex systems became evident to the broad scientific community with the publication of Strogatz’s remarkable book Sync [1]
The Decision Making Model (DMM) implements the echo response hypothesis, which assumes that the dynamic properties of a network of identical individuals are determined by singular people imperfectly copying the behavior of one another [15]
We consider the interaction between two ATA decision making model (DMM) networks each of which is modeled by a Langevin equation with a double-well potential
Summary
The significance of synchronization for the understanding of complex systems became evident to the broad scientific community with the publication of Strogatz’s remarkable book Sync [1]. Tognoli and Kelso [2] identify three types of synchrony involving relative phases between coupled regions of the brain: an inphase (zero-lag) synchronization; antiphase in which oscillatory elements have the same intrinsic frequency; and broken symmetry that is near inphase or near antiphase. Phase synchronization is a fundamental mechanism giving rise to a collective action of large ensembles of units found in near proximity to each other, which otherwise would behave according to their individual rhythms, not being able to produce a large scale response.[3]. An inphase pattern has been observed in brain activity using fMRI measurements within a cohort of patients by synchronizing brain activity across individuals watching the same movie [4]. The inphase pattern of the activity in different regions of the brain among different members of the audience cohort reveals shared emotional states
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
