1,075 research outputs found
Graph Theory and Networks in Biology
In this paper, we present a survey of the use of graph theoretical techniques
in Biology. In particular, we discuss recent work on identifying and modelling
the structure of bio-molecular networks, as well as the application of
centrality measures to interaction networks and research on the hierarchical
structure of such networks and network motifs. Work on the link between
structural network properties and dynamics is also described, with emphasis on
synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape
Synchronous chaos and broad band gamma rhythm in a minimal multi-layer model of primary visual cortex
Visually induced neuronal activity in V1 displays a marked gamma-band
component which is modulated by stimulus properties. It has been argued that
synchronized oscillations contribute to these gamma-band activity [...
however,] even when oscillations are observed, they undergo temporal
decorrelation over very few cycles. This is not easily accounted for in
previous network modeling of gamma oscillations. We argue here that
interactions between cortical layers can be responsible for this fast
decorrelation. We study a model of a V1 hypercolumn, embedding a simplified
description of the multi-layered structure of the cortex. When the stimulus
contrast is low, the induced activity is only weakly synchronous and the
network resonates transiently without developing collective oscillations. When
the contrast is high, on the other hand, the induced activity undergoes
synchronous oscillations with an irregular spatiotemporal structure expressing
a synchronous chaotic state. As a consequence the population activity undergoes
fast temporal decorrelation, with concomitant rapid damping of the oscillations
in LFPs autocorrelograms and peak broadening in LFPs power spectra. [...]
Finally, we argue that the mechanism underlying the emergence of synchronous
chaos in our model is in fact very general. It stems from the fact that gamma
oscillations induced by local delayed inhibition tend to develop chaos when
coupled by sufficiently strong excitation.Comment: 49 pages, 11 figures, 7 table
SATURATED AND ASYMMETRIC SATURATED IMPULSIVE CONTROL SYNCHRONIZATION OF COUPLED DELAYED INERTIAL NEURAL NETWORKS WITH TIME-VARYING DELAYS
This paper considers control systems with impulses that are saturated and asymmetrically saturated which are used to examine the synchronization of inertial neural networks (INNs) with time-varying delay and coupling delays. Under the theoretical discussions, mixed delays, such as transmission delay and coupling delay are presented for inertial neural networks. The addressed INNs are transformed into first order differential equations utilizing variable transformation on INNs and then certain adequate conditions are derived for the exponential synchronization of the addressed model by substituting saturation nonlinearity with a dead-zone function. In addition, an asymmetric saturated impulsive control approach is given to realize the exponential synchronization of addressed INNs in the leader-following synchronization pattern. Finally, simulation results are used to validate the theoretical research findings
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
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Synchronization Control for Discrete-Time-Delayed Dynamical Networks with Switching Topology under Actuator Saturations
10.13039/501100001809-National Natural Science Foundation of China (Grant Number: 61773156, 61873148, 61673141 and 61933007); 10.13039/501100018551-Program for Science and Technology Innovation Talents in the Universities of Henan Province of China (Grant Number: 19HASTIT028); 10.13039/501100010029-Research Fund for the Taishan Scholar Project of Shandong Province of China; 10.13039/501100000288-Royal Society of the U.K.; 10.13039/100005156-Alexander von Humboldt Foundation of Germany
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Exotic states in a simple network of nanoelectromechanical oscillators.
Synchronization of oscillators, a phenomenon found in a wide variety of natural and engineered systems, is typically understood through a reduction to a first-order phase model with simplified dynamics. Here, by exploiting the precision and flexibility of nanoelectromechanical systems, we examined the dynamics of a ring of quasi-sinusoidal oscillators at and beyond first order. Beyond first order, we found exotic states of synchronization with highly complex dynamics, including weak chimeras, decoupled states, traveling waves, and inhomogeneous synchronized states. Through theory and experiment, we show that these exotic states rely on complex interactions emerging out of networks with simple linear nearest-neighbor coupling. This work provides insight into the dynamical richness of complex systems with weak nonlinearities and local interactions
Dynamics of biologically informed neural mass models of the brain
This book contributes to the development and analysis of computational models that help brain function to be understood. The mean activity of a brain area is mathematically modeled in such a way as to strike a balance between tractability and biological plausibility. Neural mass models (NMM) are used to describe switching between qualitatively different regimes (such as those due to pharmacological interventions, epilepsy, sleep, or context-induced state changes), and to explain resonance phenomena in a photic driving experiment. The description of varying states in an ordered sequence gives a principle scheme for the modeling of complex phenomena on multiple time scales. The NMM is matched to the photic driving experiment routinely applied in the diagnosis of such diseases as epilepsy, migraine, schizophrenia and depression. The model reproduces the clinically relevant entrainment effect and predictions are made for improving the experimental setting.Die vorliegende Arbeit stellt einen Beitrag zur Entwicklung und Analyse von
Computermodellen zum Verständnis von Hirnfunktionen dar. Es wird die
mittlere Aktivität eines Hirnareals analytisch einfach und dabei
biologisch plausibel modelliert. Auf Grundlage eines Neuronalen
Massenmodells (NMM) werden die Wechsel zwischen Oszillationsregimen (z.B.
durch pharmakologisch, epilepsie-, schlaf- oder kontextbedingte
Zustandsänderungen) als geordnete Folge beschrieben und Resonanzphänomene
in einem Photic-Driving-Experiment erklärt. Dieses NMM kann sehr komplexe
Dynamiken (z.B. Chaos) innerhalb biologisch plausibler Parameterbereiche
hervorbringen. Um das Verhalten abzuschätzen, wird das NMM als Funktion
konstanter Eingangsgrößen und charakteristischer Zeitenkonstanten
vollständig auf Bifurkationen untersucht und klassifiziert. Dies
ermöglicht die Beschreibung wechselnder Regime als geordnete Folge durch
spezifische Eingangstrajektorien. Es wird ein Prinzip vorgestellt, um
komplexe Phänomene durch Prozesse verschiedener Zeitskalen darzustellen.
Da aufgrund rhythmischer Stimuli und der intrinsischen Rhythmen von
Neuronenverbänden die Eingangsgrößen häufig periodisch sind, wird das
Verhalten des NMM als Funktion der Intensität und Frequenz einer
periodischen Stimulation mittels der zugehörigen Lyapunov-Spektren und der
Zeitreihen charakterisiert. Auf der Basis der größten Lyapunov-Exponenten
wird das NMM mit dem Photic-Driving-Experiment überein gebracht. Dieses
Experiment findet routinemäßige Anwendung in der Diagnostik verschiedener
Erkrankungen wie Epilepsie, Migräne, Schizophrenie und Depression. Durch
die Anwendung des vorgestellten NMM wird der für die Diagnostik
entscheidende Mitnahmeeffekt reproduziert und es werden Vorhersagen für
eine Verbesserung der Indikation getroffen
Distributed Control of Networked Nonlinear Euler-Lagrange Systems
Motivated by recent developments in formation and cooperative control of networked multi-agent systems, the main goal of this thesis is development of efficient synchronization and formation control algorithms for distributed control of networked nonlinear systems whose dynamics can be described by Euler-Lagrange (EL) equations. One of the main challenges in the design of the formation control algorithm is its optimality and robustness to parametric uncertainties, external disturbances and ability to reconfigure in presence of component, actuator, or sensor faults. Furthermore, the controller should be capable of handling switchings in the communication network topology.
In this work, nonlinear optimal control techniques are studied for developing distributed controllers for networked EL systems. An individual cost function is introduced to design a controller that relies on only local information exchanges among the agents. In the development of the controller, it is assumed that the communication graph is not fixed (in other words the topology is switching). Additionally, parametric uncertainties and faults in the EL systems are considered and two approaches, namely adaptive and robust techniques are introduced to compensate for the effects of uncertainties and actuator faults.
Next, a distributed H_infinity performance measure is considered to develop distributed robust controllers for uncertain networked EL systems. The developed distributed controller is obtained through rigorous analysis and by considering an individual cost function to enhance the robustness of the controllers in presence of parametric uncertainties and external bounded disturbances. Moreover, a rigorous analysis is conducted on the performance of the developed controllers in presence of actuator faults as well as fault diagnostic and identification (FDI) imperfections.
Next, synchronization and set-point tracking control of networked EL systems are investigated in presence of three constraints, namely, (i) input saturation constraints, (ii) unavailability of velocity feedback, and (iii) lack of knowledge on the system parameters. It is shown that the developed distributed controllers can accomplish the desired requirements and specification under the above constraints.
Finally, a quaternion-based approach is considered for the attitude synchronization and set-point tracking control problem of formation flying spacecraft. Employing the quaternion in the control law design enables handling large rotations in the spacecraft attitude and, therefore, any singularities in the control laws are avoided. Furthermore, using the quaternion also enables one to guarantee boundedness of the control signals both with and without velocity feedback
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