Winnie Poel

Bio: Winnie Poel is an academic researcher from Technical University of Berlin. The author has contributed to research in topics: Network topology & Amplitude death. The author has an hindex of 3, co-authored 7 publications receiving 108 citations. Previous affiliations of Winnie Poel include Humboldt University of Berlin.

Individual and collective encoding of risk in animal groups.

Abstract: The need to make fast decisions under risky and uncertain conditions is a widespread problem in the natural world. While there has been extensive work on how individual organisms dynamically modify their behavior to respond appropriately to changing environmental conditions (and how this is encoded in the brain), we know remarkably little about the corresponding aspects of collective information processing in animal groups. For example, many groups appear to show increased “sensitivity” in the presence of perceived threat, as evidenced by the increased frequency and magnitude of repeated cascading waves of behavioral change often observed in fish schools and bird flocks under such circumstances. How such context-dependent changes in collective sensitivity are mediated, however, is unknown. Here we address this question using schooling fish as a model system, focusing on 2 nonexclusive hypotheses: 1) that changes in collective responsiveness result from changes in how individuals respond to social cues (i.e., changes to the properties of the “nodes” in the social network), and 2) that they result from changes made to the structural connectivity of the network itself (i.e., the computation is encoded in the “edges” of the network). We find that despite the fact that perceived risk increases the probability for individuals to initiate an alarm, the context-dependent change in collective sensitivity predominantly results not from changes in how individuals respond to social cues, but instead from how individuals modify the spatial structure, and correspondingly the topology of the network of interactions, within the group. Risk is thus encoded as a collective property, emphasizing that in group-living species individual fitness can depend strongly on coupling between scales of behavioral organization.

Synchronization patterns: from network motifs to hierarchical networks

Abstract: We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart–Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is motivated by the network of neurons in the brain. This fractal property is well represented in hierarchical networks, for which we present three different models. In addition, we introduce an analytical eigensolution method and provide a comprehensive picture of the interplay of network topology and the corresponding network dynamics, thus allowing us to predict the dynamics of arbitrarily large hierarchical networks simply by analysing small network motifs. We also show that oscillation death can be induced in these networks, even if the coupling is symmetric, contrary to previous understanding of oscillation death. Our results show that there is a direct correlation between topology and dynamics: hierarchical networks exhibit the corresponding hierarchical dynamics. This helps bridge the gap between mesoscale motifs and macroscopic networks. This article is part of the themed issue ‘Horizons of cybernetical physics’.

Partial synchronization and partial amplitude death in mesoscale network motifs.

Abstract: We study the interplay between network topology and complex space-time patterns and introduce a concept to analytically predict complex patterns in networks of Stuart-Landau oscillators with linear symmetric and instantaneous coupling based solely on the network topology. These patterns consist of partial amplitude death and partial synchronization and are found to exist in large variety for all undirected networks of up to 5 nodes. The underlying concept is proved to be robust with respect to frequency mismatch and can also be extended to larger networks. In addition it directly links the stability of complete in-phase synchronization to only a small subset of topological eigenvalues of a network.

Spatial Structure and Information Transfer in Visual Networks

Abstract: In human and animal groups, social interactions often rely on the transmission of information via visual observation of the behavior of others. These visual interactions are governed by the laws of physics and sensory limits. Individuals appear smaller when far away and thus become harder to detect visually, while close by neighbors tend to occlude large areas of the visual field and block out interactions with individuals behind them. Here, we systematically study the effect of a group's spatial structure, its density as well as polarization and aspect ratio of the physical bodies, on the properties of the visual interaction network. In such a network individuals are connected if they can see each other as opposed to other interaction models such as metric or topological networks that omit these limitations due to the individual's physical bodies. We study the effect that spatial configuration has on the static properties of these networks as well as its influence on the transmission of information or behaviors which we investigate via two generic models of social contagion. We expect our work to have implications for the study of animal groups, where it could inform the study of functional benefits of different macroscopic states. It may also be applicable to the construction of robotic swarms communicating via vision or for understanding the spread of panics in human crowds.

Subcritical escape waves in schooling fish

Abstract: Living systems such as neuronal networks and animal groups process information about their environment via the dynamics of interacting units. These can transition between distinct macroscopic behaviors. Near such a transition (or critical point) collective computation is generally thought to be optimized, due to the associated maximal sensitivity to perturbations and fast dissemination of information. For biological systems, however, optimality depends on environmental context, making the flexible, context-dependent adoption of different distances to a critical point potentially more beneficial than its unique properties. Here, studying escape waves in schooling fish at two levels of perceived environmental risk, we investigate a) if and how distance to criticality is regulated in response to environmental changes and b) how the individual level benefits derived from special properties of the critical point compare to those achieved via regulation of the group's distance to it. We find that the observed fish schools are subcritical (not maximally responsive and sensitive to environmental cues), but decrease their distance to criticality with increased perceived risk. Considering an individual's hypothetical costs of two detection error types, we find that optimal distance to criticality depends on the riskiness and noisiness of the environment, which may explain the observed behavior. Our results highlight the benefit of evaluating biological consequences of different distances to criticality for individuals within animal collectives. This provides insights into the adaptive function of a collective system and motivates future questions about the evolutionary forces that brought the system to make this particular trade-off.

Complete characterization of the stability of cluster synchronization in complex dynamical networks

Abstract: Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted to admit global synchronization, a condition called Laplacian coupling. Many networks exhibit incomplete synchronization, where two or more clusters of synchronization persist, and computational group theory has recently proved to be valuable in discovering these cluster states based on the topology of the network. In the important case of Laplacian coupling, additional synchronization patterns can exist that would not be predicted from the group theory analysis alone. Understanding how and when clusters form, merge, and persist is essential for understanding collective dynamics, synchronization, and failure mechanisms of complex networks such as electric power grids, distributed control networks, and autonomous swarming vehicles. We describe a method to find and analyze all of the possible cluster synchronization patterns in a Laplacian-coupled network, by applying methods of computational group theory to dynamically equivalent networks. We present a general technique to evaluate the stability of each of the dynamically valid cluster synchronization patterns. Our results are validated in an optoelectronic experiment on a five-node network that confirms the synchronization patterns predicted by the theory.

Synchronization patterns and chimera states in complex networks: Interplay of topology and dynamics

Abstract: We review chimera patterns, which consist of coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics in networks of identical oscillators. We focus on chimera states involving amplitude as well as phase dynamics, complex topologies like small-world or hierarchical (fractal), noise, and delay. We show that a plethora of novel chimera patterns arise if one goes beyond the Kuramoto phase oscillator model. For the FitzHugh-Nagumo system, the Van der Pol oscillator, and the Stuart-Landau oscillator with symmetry-breaking coupling various multi-chimera patterns including amplitude chimeras and chimera death occur. To test the robustness of chimera patterns with respect to changes in the structure of the network, regular rings with coupling range R, small-world, and fractal topologies are studied. We also address the robustness of amplitude chimera states in the presence of noise. If delay is added, the lifetime of transient chimeras can be drastically increased.

Chimera states in brain networks: Empirical neural vs. modular fractal connectivity

Abstract: Complex spatiotemporal patterns, called chimera states, consist of coexisting coherent and incoherent domains and can be observed in networks of coupled oscillators. The interplay of synchrony and asynchrony in complex brain networks is an important aspect in studies of both the brain function and disease. We analyse the collective dynamics of FitzHugh-Nagumo neurons in complex networks motivated by its potential application to epileptology and epilepsy surgery. We compare two topologies: an empirical structural neural connectivity derived from diffusion-weighted magnetic resonance imaging and a mathematically constructed network with modular fractal connectivity. We analyse the properties of chimeras and partially synchronized states and obtain regions of their stability in the parameter planes. Furthermore, we qualitatively simulate the dynamics of epileptic seizures and study the influence of the removal of nodes on the network synchronizability, which can be useful for applications to epileptic surgery.