Articles
Chaos, Solitons and Fractals (09600779)
We investigate how modular and hierarchical delay structures shape synchronization dynamics in networks of uniformly connected phase oscillators. Using a Kuramoto model adapted to incorporate modular interaction delays, we isolate the effects of temporal heterogeneity from structural modularity. Our analysis identifies distinct synchronization regimes dependent on oscillator frequency: global coherence at low frequencies, modular synchronization at intermediate frequencies, and incoherence dominates at high frequencies, though localized coherence can reemerge under specific delay configurations. Under hierarchical delay arrangements, we further observe a reemergence of localized coherence within sub-modules at very high frequencies, indicating multi-scale synchronization facilitated purely by temporal delays. These findings highlight the fundamental role modular and hierarchical delays play in shaping functional network dynamics, offering insights relevant to the adaptability and multi-scale processing capabilities observed in neural and technological systems. © 2025 Elsevier Ltd
Nonlinear Dynamics (0924090X)(3)
Brain networks are characterized by flexible patterns of pairwise correlations and information exchange between different brain regions. Such dynamic patterns are crucial for an efficient response of the brain to environmental and cognitive demands. We here propose that the collective oscillations in the brain can provide a mechanism to control dynamical interactions and the exchange of information across brain networks. In particular, we show that the phase difference between oscillatory activities in different brain regions determines the transmission of neural signals. To further corroborate this, we study a network of coupled oscillators with repulsive couplings and show that the amount of information transfer between the nodes is determined by the phase differences. The emergence of multiple (locally) stable states due to the frustration makes it possible to change the patterns of information transfer between the nodes by means of the switching between different stable states. Our results indicate that frustration can be the mechanism through which large-scale brain networks control the effective connectivity and the routes for the information transfer between different brain regions. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.
We investigate the impact of a stochastic forcing, comprised of a sum of time-lagged copies of a single source of noise, on the system dynamics. This type of stochastic forcing could be made artificially, or it could be the result of shared upstream inputs to a system through different channel lengths. By means of a rigorous mathematical framework, we show that such a system is, in fact, equivalent to the classical case of a stochastically-driven dynamical system with time-delayed intrinsic dynamics but without a time lag in the input noise. We also observe a resonancelike effect between the intrinsic period of the oscillation and the time lag of the stochastic forcing, which may be used to determine the intrinsic period of oscillations or the inherent time delay in dynamical systems with oscillatory behavior or delays. As another useful application of imposing time-lagged stochastic forcing, we show that the dynamics of a system can be controlled by changing the time lag of this stochastic forcing, in a fashion similar to the classical case of Pyragas control via delayed feedback. To confirm these results experimentally, we set up a laser diode system with such stochastic inputs, which effectively behaves as a Langevin system. As in the theory, a peak emerged in the autocorrelation function of the output signal that could be tuned by the lag of the stochastic input. Our findings, thus, indicate a new approach for controlling useful instabilities in dynamical systems. © 2020 Author(s).
