Flatness-based real-time control of experimental analog chaotic oscillators

Minati, Ludovico; Frasca, Mattia; Valdes-Sosa, Pedro A.; Barbot, Jean-Pierre; Letellier, Christophe

doi:10.1016/j.chaos.2023.114274

Cited by 5 publications

(3 citation statements)

References 55 publications

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“…e −µ , where µ = ρ(t)δ bin and ρ(t) is constant over time, then F = 1. If on the other hand, ρ(t) changes in time, and time bin δ bin is larger than the autocorrelation time of ρ(t), then the Fano is proportional to such autocorrelation time, as discussed in [12]. A long autocorrelation time in ρ(t) reflects into F ≫ 1.…”

Section: Methodsmentioning

confidence: 97%

“…We hypothesize that the microscopic dynamics should operate in, or near, a critical regime for the functional repertoire to be effectively explored and for realistic flexible dynamics to emerge. A long-held theory posits that the brain self-organizes into a critical regime near the edge of a dynamical phase transition [5][6][7][8][9], where the balance between global inhibition and excitation plays a crucial role [10][11][12], and possibly leading to functional optimality [10,[13][14][15][16][17][18][19]. It has been proposed that the brain experiences both continuous phase transitions with scale-free avalanches, and discontinuous transitions, which are beneficial for self-sustained replay activity and memory functioning [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Criticality explains structure-function relationships in the human brain

Angiolelli,

Scarpetta,

Sorrentino

et al. 2024

Preprint

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Healthy brain exhibits a rich dynamical repertoire, with flexible spatiotemporal patterns replays on both microscopic and macroscopic scales. How do fixed structural connections yield a diverse range of dynamic patterns in spontaneous brain activity? We hypothesize that the observed relationship between empirical structure and functional patterns is best explained when the microscopic neuronal dynamics is close to a critical regime. Using a modular Spiking Neuronal Network model based on empirical connectomes, we posit that multiple stored functional patterns can transiently reoccur when the system operates near a critical regime, generating realistic brain dynamics and structural-functional relationships. The connections in the model are chosen as to force the network to learn and propagate suited modular spatiotemporal patterns. To test our hypothesis, we employ magnetoencephalography and tractography data from five healthy individuals. We show that the critical regime of the model is able to generate realistic features, and demonstrate the relevance of near-critical regimes for physiological brain activity.

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Section: Methodsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Criticality explains structure-function relationships in the human brain

Angiolelli,

Scarpetta,

Sorrentino

et al. 2024

Preprint

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“…The two measured variables are still y R and y S . As investigated in a previous work [62], the actuating signal u given by Eq. ( 30) is applied to the derivative ẇS .…”

Section: E Rössler Driving Saitomentioning

confidence: 99%

Node differentiation dynamics along the route to synchronization in complex networks

et al. 2021

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Generalized synchronization is plausibly the most complex form of synchronization. Previous studies have revealed the existence of weak or strong forms of generalized synchronization depending on the multi-or mono-valued nature of the mapping between the attractors of two unidirectionallycoupled systems. Generalized synchronization is here obtained by coupling two systems with a flat control law. Here, we demonstrate that the corresponding first-return maps can be topologically conjugate in some cases. Conversely, the response map can foliated while the drive map is not. We describe the corresponding types of generalized synchronization, explicitly focusing on the influence of the coupling strength when significantly different dimensions or dissipation properties characterize the coupled systems. A taxonomy of generalized synchronization based on these properties is proposed.

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