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Article
Open AccessModeling brain network flexibility in networks of coupled oscillators: a feasibility study
Modeling the functionality of the human brain is a major goal in neuroscience for which many powerful methodologies have been developed over the last decade. The impact of working memory and the associated br...
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Article
Phase response approaches to neural activity models with distributed delay
In weakly coupled neural oscillator networks describing brain dynamics, the coupling delay is often distributed. We present a theoretical framework to calculate the phase response curve of distributed-delay in...
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Chapter
Reservoir Computing Using Autonomous Boolean Networks Realized on Field-Programmable Gate Arrays
In this chapter, we consider realizing a reservoir computer on an electronic chip that allows for many tens of network nodes whose connection topology can be quickly reconfigured. The reservoir computer displa...
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Article
Open AccessSolitary states in adaptive nonlocal oscillator networks
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an...
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Article
Nonlinear excitations and bound states of electrons, holes and solitons in bilayers of triangular lattices
We study the temporal and spatial nonlinear dynamical evolution of a coupled triangular lattice crystal bilayer system where in one layer one excess free electron is injected while an excess positive charge, a...
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Article
Synchronization patterns in Stuart–Landau networks: a reduced system approach
We study networks with coupled phase and amplitude dynamics. In particular, we investigate a ring of Stuart–Landau oscillators. For symmetry-conserving coupling we observe cluster synchronization. We show tha...
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Article
Delay-induced chimeras in neural networks with fractal topology
We study chimera states, which are partial synchronization patterns consisting of spatially coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics, in ring networks of FitzHugh...
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Article
Synchronization scenarios of chimeras in multiplex networks
Complex networks consisting of several interacting layers allow for remote synchronization of distant layers via an intermediate relay layer. We extend the notion of relay synchronization to chimera states, a...
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Article
Open AccessWhy more physics can help achieving better mathematics
In this paper, we discuss the question whether a physical “simplification” of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different e...
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Article
Chimera states in networks of logistic maps with hierarchical connectivities
Chimera states are complex spatiotemporal patterns consisting of coexisting domains of coherence and incoherence. We study networks of nonlocally coupled logistic maps and analyze systematically how the dilut...
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Article
Synchronization of organ pipes
We investigate synchronization of coupled organ pipes. Synchronization and reflection in the organ lead to undesired weakening of the sound in special cases. Recent experiments have shown that sound interacti...
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Article
Chimeras in leaky integrate-and-fire neural networks: effects of reflecting connectivities
The effects of attracting-nonlocal and reflecting connectivity are investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which model the exchange of electrical signals between neurons. Earlier inve...
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Article
Chimera states in complex networks: interplay of fractal topology and delay
Chimera states are an example of intriguing partial synchronization patterns emerging in networks of identical oscillators. They consist of spatially coexisting domains of coherent (synchronized) and incohere...
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Chapter and Conference Paper
Noise-Induced Chimera States in a Neural Network
We show that chimera patterns can be induced by noise in nonlocally coupled neural networks in the excitable regime. In contrast to classical chimeras, occurring in noise-free oscillatory networks, they have f...
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Article
Optimization of nonlocal time-delayed feedback controllers
A class of Pyragas type nonlocal feedback controllers with time-delay is investigated for the Schlögl model. The main goal is to find an optimal kernel in the controller such that the associated solution of th...
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Article
Optimal and resonant time-delayed feedback control of unstable steady states: self-adaptive tuning of coupling phase
We suggest an optimized scheme for the time-delayed feedback control of an unstable fixed point. For the normal form of an unstable focus, we derive the optimal feedback phase that yields the strongest stabili...
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Book
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Chapter and Conference Paper
Control of Desynchronization Transitions in Delay-Coupled Networks of Type-I and Type-II Excitable Systems
We discuss synchronization and desynchronization transitions in networks of delay-coupled excitable systems. These transitions arise in response to varying the balance of excitatory and inhibitory couplings in...
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Chapter
Controlling Chimera Patterns in Networks: Interplay of Structure, Noise, and Delay
We investigate partially coherent and partially incoherent patterns (chimera states) in networks of Stuart-Landau oscillators with symmetry-breaking coupling. In particular, we study two types of chimera state...
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Chapter
Adaptively Controlled Synchronization of Delay-Coupled Networks
We discuss an adaptive control delay-coupled networks of Stuart-Landau oscillators, an expansion of systems close to a Hopf bifurcation. Based on the considered, automated control scheme, the speed-gradient me...
