650 citations · 2.4k across the 32 of their papers we have counts for
24 papers · 1 filter
Self-organizing Chimera States in Adaptive Networks
Felix Augustsson, Rok Cestnik, Matthias Wolfrum +3
We propose a minimal adaptive network model with product-form coupling that reduces dimensionality while capturing key features of synaptic plasticity. The system spontaneously sel…
Multiple Timescale Dynamics of Network Adaptation with Constraints
Erik Andreas Martens, Christian Bick
Adaptive network dynamical systems describe the co-evolution of dynamical quantities on the nodes as well as dynamics of the network connections themselves. For dense networks of m…
Non-local transitions and ground state switching in the self-organization of vascular networks
Konstantin Klemm, Erik Andreas Martens
The model by Hu and Cai [Phys. Rev. Lett., Vol. 111(13) (2013)] describes the self-organization of vascular networks for transport of fluids from source to sinks. Diameters, and th…
Continuum limit of the adaptive Kuramoto model
Rok Cestnik, Erik A. Martens
We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, . This model is distinguished by dense multistability, where mul…
Inverse stochastic resonance in adaptive small-world neural networks
Marius E. Yamakou, Jinjie Zhu, Erik A. Martens
Inverse stochastic resonance (ISR) is a phenomenon where noise reduces rather than increases the firing rate of a neuron, sometimes leading to complete quiescence. ISR was first ex…
Co-evolutionary dynamics for two adaptively coupled Theta neurons
Felix Augustsson, Erik Andreas Martens
Natural and technological networks exhibit dynamics that can lead to complex cooperative behaviors, such as synchronization in coupled oscillators and rhythmic activity in neuronal…
Bifurcations in adaptive vascular networks: towards model calibration
Konstantin Klemm, Erik Andreas Martens
Transport networks are crucial for the functioning of natural and technological systems. We study a mathematical model of vascular network adaptation, where the network structure d…
Integrability of a globally coupled complex Riccati array: quadratic integrate-and-fire neurons, phase oscillators and all in between
Rok Cestnik, Erik A. Martens
We present an exact dimensionality reduction for dynamics of an arbitrary array of globally coupled complex-valued Riccati equations. It generalizes the Watanabe-Strogatz theory [P…
Complex dynamics in adaptive phase oscillator networks
Benjamin Jüttner, Erik Andreas Martens
Networks of coupled dynamical units give rise to collective dynamics such as the synchronization of oscillators or neurons in the brain. The ability of the network to adapt couplin…
Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators
Oleksandr Burylko, Erik Andreas Martens, Christian Bick
Despite their simplicity, networks of coupled phase oscillators can give rise to intriguing collective dynamical phenomena. However, the symmetries of globally and identically coup…
Graphop Mean-Field Limits and Synchronization for the Stochastic Kuramoto Model
Marios Antonios Gkogkas, Benjamin Jüttner, Christian Kuehn +1
Models of coupled oscillator networks play an important role in describing collective synchronization dynamics in biological and technological systems. The Kuramoto model describes…
First-order like phase transition induced by quenched coupling disorder
Hyunsuk Hong, Erik Andreas Martens
We investigate the collective dynamics of a population of XY model-type oscillators, globally coupled via non-separable interactions that are randomly chosen from a positive or neg…
A Two-Frequency-Two-Coupling model of coupled oscillators
Hyunsuk Hong, Erik A. Martens
We considered the phase coherence dynamics in a Two-Frequency and Two-Coupling (TFTC) model of coupled oscillators, where coupling strength and natural oscillator frequencies for i…
Birth and destruction of collective oscillations in a network of two populations of coupled type 1 neurons
Benjamin Jüttner, Christian Henriksen, Erik A. Martens
We study the macroscopic dynamics of large networks of excitable type 1 neurons composed of two populations interacting with disparate but symmetric intra- and inter-population cou…
Directed Flow of Information in Chimera States
Nicolás Deschle, Andreas Daffertshofer, Demian Battaglia +1
We investigated interactions within chimera states in a phase oscillator network with two coupled subpopulations. To quantify interactions within and between these subpopulations,…
Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
Christian Bick, Marc Goodfellow, Carlo R. Laing +1
Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, their functionality depends on the emerging collective dynamics of the ne…
First-order synchronization transition in a large population of strongly coupled relaxation oscillators
Dumitru Călugăru, Jan Frederik Totz, Erik A. Martens +1
Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural n…
Cyclic structure induced by load fluctuations in adaptive transportation networks
Erik Andreas Martens, Konstantin Klemm
Transport networks are crucial to the functioning of natural systems and technological infrastructures. For flow networks in many scenarios, such as rivers or blood vessels, acycli…
Transitions from trees to cycles in adaptive flow networks
Erik Andreas Martens, Konstantin Klemm
Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus p…
Chimera states in two populations with heterogeneous phase-lag
Erik Andreas Martens, Christian Bick, Mark J Panaggio
The simplest network of coupled phase-oscillators exhibiting chimera states is given by two populations with disparate intra- and inter-population coupling strengths. We explore th…
Controlling Chimeras
Christian Bick, Erik A. Martens
Coupled phase oscillators model a variety of dynamical phenomena in nature and technological applications. Non-local coupling gives rise to chimera states which are characterized b…
Chimera States in Mechanical Oscillator Networks
Erik Andreas Martens, Shashi Thutupalli, Antoine Fourrière +1
The synchronization of coupled oscillators is a fascinating manifestation of self-organization that nature employs to orchestrate essential processes of life, such as the beating o…
Bistable Chimera Attractors on a Triangular Network of Oscillator Populations
Erik Andreas Martens
We study a triangular network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators a…
Chimeras in a Network of Three Oscillator Populations with Varying Network Topology
Erik Andreas Martens
We study a network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled…