# Nonlinear Sciences - Adaptation and Self-Organizing Systems Publications (50)

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## Nonlinear Sciences - Adaptation and Self-Organizing Systems Publications

**Affiliations:**

^{1}MAMBA, LJLL

Collective motion of chemotactic bacteria as E. Coli relies, at the individual level, on a continuous reorientation by runs and tumbles. It has been established that the length of run is decided by a stiff response to temporal sensing of chemical cues along the pathway. Read More

We demonstrate the application of the multiplex networks-approach for the analysis of various networks which connected individuals and communities in the politically highly fragmented late medieval Balkans (1204-1453 AD) within and across border zones. We present how we obtain relational data from our sources and the integration of these data into three different networks (of roads, state administration and ecclesiastical administration) of various topologies; then we calculate several indicators for influences and overlaps between these different networks which connect the same set of nodes (settlements). We analyse changes and continuities in the topologies of the various networks for three time-steps (1210, 1324 and 1380 CE) and demonstrate the role of these networks as frameworks for social interactions. Read More

Recently the dynamics of signed networks, where the ties among the agents can be both positive (attractive) or negative (repulsive) have attracted substantial attention of the research community. Examples of such networks are models of opinion dynamics over signed graphs, recently introduced by Altafini (2012,2013) and extended to discrete-time case by Meng et al. (2014). Read More

Many problems in industry --- and in the social, natural, information, and medical sciences --- involve discrete data and benefit from approaches from subjects such as network science, information theory, optimization, probability, and statistics. Because the study of networks is concerned explicitly with connectivity between different entities, it has become very prominent in industrial settings, and this importance has been accentuated further amidst the modern data deluge. In this article, we discuss the role of network analysis in industrial and applied mathematics, and we give several examples of network science in industry. Read More

The spider silk is one of the most interesting bio-materials investigated in the last years. One of the main reasons that brought scientists to study this organized system is its high level of resistance if compared to other artificial materials characterized by higher density. Subsequently, researchers discovered that the spider silk is a complex system formed by different kinds of proteins, organized (or disorganized) to guarantee the required resistance, which is function of the final application and of the environmental conditions. Read More

Many coordination phenomena in Nature are grounded on a synchronisation regime. In the case of brain dynamics, such self-organised process allows the neurons of particular brain regions to behave as a whole and thus directly controlling the neural activity, the muscles and finally the whole human body. However, not always such synchronised collective behaviour is the desired one, this is the case of neurodegenerative diseases such as Parkinson's or epilepsy where abnormal synchronisation induces undesired effects such as tremors and epileptic seizures. Read More

The vortices that appear repeatedly and suggest turbulent dynamics are crucial to the understanding of sheared turbulence. These vortices produce order out of chaos, benefiting the turbulence modelling that focuses only on statistically stable quantities. In three dimensions, the hairpin vortices play such a fundamental role in the transport of momentum and energy for wall bounded sheared turbulence. Read More

Spontaneous symmetry breaking (SSB) is an important phenomenon observed in various fields including physics and biology. In this connection, we here show that the trade-off between attractive and repulsive couplings can induce spontaneous symmetry breaking in a homogeneous system of coupled oscillators. With a simple model of a system of two coupled Stuart-Landau oscillators, we demonstrate how the tendency of attractive coupling in inducing in-phase synchronized (IPS) oscillations and the tendency of repulsive coupling in inducing out-of-phase synchronized (OPS) oscillations compete with each other and give rise to symmetry breaking oscillatory (SBO) states and interesting multistabilities. Read More

We propose a model of an adaptive network of spiking neurons that gives rise to a hypernetwork of its dynamic states at the upper level of description. Left to itself, the network exhibits a sequence of transient clustering which relates to a traffic in the hypernetwork in the form of a random walk. Receiving inputs the system is able to generate reproducible sequences corresponding to stimulus-specific paths in the hypernetwork. Read More

Phase response curve (PRC) is an extremely useful tool for studying the response of oscillatory systems, e.g. neurons, to sparse or weak stimulation. Read More

Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether such scaling laws stem from the underlying neural dynamics operating at the edge of a phase transition is a fascinating possibility, as systems poised at criticality have been argued to exhibit a number of important functional advantages. Here we employ a well-known model for neural dynamics with synaptic plasticity, to elucidate an alternative scenario in which neuronal avalanches can coexist, overlapping in time, but still remaining scale-free. Read More

Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively investigated, little is known about a general mechanism for achieving robustness in reaction-diffusion systems. Here, we propose a buffered reaction-diffusion system, in which active states of chemicals mediated by buffer molecules contribute to reactions, and demonstrate that robustness of the pattern wavelength is achieved by the dynamics of the buffer molecule. Read More

Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre-synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post-synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Read More

Living organisms, ecosystems, and social systems are examples of complex systems in which robustness against inclusion of new elements is an essential feature. A recently proposed simple model has revealed a general mechanism by which such systems can become robust against inclusion of elements with random interactions when the elements have a moderate number of links. This happens as a result of two opposing effects such that while the inclusion of elements with more interactions makes each individual element more robust against disturbances, it also increases the net impact of the loss of any element in the system. Read More

A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust inter-nodes correlations, that persist at large large distances. Anti-phase synchrony at small frequencies is resolved on adjacent nodes and found to promote the spontaneous generation of long-ranged stochastic patterns, that invade the network as a whole. Read More

The Wikipedia is a web portal created by users and its simplicity, references and also the inclusion as insets introductory paragraphs for their pages in Google search results have made it the go-to place to find out about current events or people featured in them. Besides, its open application programming interface (API) allows any user to know about the number of visits some particular page has. In this paper, after certain events that made Copernicus a viral meme in Spain, we study the intensity and duration of the increment of visits to his page and other pages related to the event. Read More

Functional oscillator networks, such as neuronal networks in the brain, exhibit switching between metastable states involving many oscillators. Chimeras - localized frequency synchrony patterns - are candidates for such states, but their spatial location has predominantly been considered fixed. We show that dynamical transitions of the location of frequency synchrony arise in paradigmatic phase oscillator networks through metastable chimeras joined by heteroclinic connections. Read More

The rising complexity of our terrestrial surrounding is an empirical fact. Details of this process evaded description in terms of physics for long time attracting attention and creating myriad of ideas including non-scientific ones. In this essay we explain the phenomenon of the growth of complexity by combining our up to date understanding of cosmology, non-equilibrium physics and thermodynamics. Read More

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 incoherent (desynchronized) dynamics. We analyze chimera states in networks of Van der Pol oscillators with hierarchical connectivities, and elaborate the role of time delay introduced in the coupling term. Read More

Digital memcomputing machines (DMMs) are non-linear dynamical systems designed so that their equilibrium points are solutions of the Boolean problem they solve. In a previous work [Chaos 27, 023107 (2017)] it was argued that when DMMs support solutions of the associated Boolean problem then strange attractors cannot coexist with such equilibria. In this work, we demonstrate such conjecture. Read More

**Authors:**Nima Dehghani

Our desire and fascination with intelligent machines dates back to the antiquity's mythical automaton Talos, Aristotle's mode of mechanical thought (syllogism) and Heron of Alexandria's mechanical machines and automata. However, the quest for Artificial General Intelligence (AGI) is troubled with repeated failures of strategies and approaches throughout the history. This decade has seen a shift in interest towards bio-inspired software and hardware, with the assumption that such mimicry entails intelligence. Read More

We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitatively account for stability and bifurcations of the exact system, capturing all the generic forms of collective behavior, including macroscopic excitability, subthreshold oscillations, periodic or chaotic spiking and chaotic bursting dynamics. Apart from qualitative analogies, we find a substantial quantitative agreement between the exact and the approximate system, as reflected in matching of the parameter domains admitting the different dynamical regimes, as well as the characteristic properties of the associated time series. Read More

We consider extended starlike networks where the hub node is coupled with several chains of nodes representing star rays. Assuming that nodes of the network are occupied by nonidentical self-oscillators we study various forms of their cluster synchronization. Radial cluster emerges when the nodes are synchronized along a ray, while circular cluster is formed by nodes without immediate connections but located on identical distances to the hub. Read More

A combination of a priority queueing model and mean field theory shows the emergence of traders' swarm behavior, even when each has a subjective prediction of the market driven by a limit order book. Using a nonlinear Markov model, we analyze the dynamics of traders who select a favorable order price taking into account the waiting cost incurred by others. We find swarm behavior emerges because of the delay in trader reactions to the market, and the direction of the swarm is decided by the current market position and the intensity of zero-intelligent random behavior, rather than subjective trader predictions. Read More

Understanding the influence of structure of dispersal network on the species persistence and modeling a much realistic species dispersal in nature are two central issues in spatial ecology. A realistic dispersal structure which favors the persistence of interacting ecological systems has been studied in [Holland \& Hastings, Nature, 456:792--795 (2008)], where it is shown that a randomization of the structure of dispersal network in a metapopulation model of prey and predator increases the species persistence via clustering, prolonged transient dynamics, and amplitudes of population fluctuations. In this paper, by contrast, we show that a deterministic network topology in a metapopulation can also favor asynchrony and prolonged transient dynamics if species dispersal obeys a long-range interaction governed by a distance-dependent power-law. Read More

The geographical pattern of human dialects is a result of history. Here, we formulate a simple spatial model of language change which shows that the final result of this historical evolution may, to some extent, be predictable. The model shows that the boundaries of language dialect regions are controlled by a length minimizing effect analogous to surface tension, mediated by variations in population density which can induce curvature, and by the shape of coastline or similar borders. Read More

Recently, the explosive phase transitions, such as explosive percolation and explosive synchronization, have attracted extensive research interest. So far, most existing works investigate Kuramoto-type models, where only phase variables are involved. Here, we report the occurrence of explosive oscillation quenching in a system of coupled Stuart-Landau oscillators that incorporates both phase and amplitude dynamics. Read More

We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles, and disappears in the thermodynamic limit. For all considered setups, that include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size. Read More

80% of all Renewable Energy Power in Germany is installed in tree-like distribution grids. Intermittent power fluctuations from such sources introduce new dynamics into the lower grid layers. At the same time, distributed resources will have to contribute to stabilize the grid against these fluctuations in the future. Read More

Synchronization in a frequency-weighted Kuramoto model with a uniform frequency distribution is studied. We plot the bifurcation diagram and identify the asymptotic coherent states. Numerical simulations show that the system undergoes two first-order transitions in both the forward and backward directions. Read More

In this work, we study the dynamical robustness in a system consisting of both active and inactive oscillators. We analytically show that the dynamical robustness of such system is determined by the cross link density between active and inactive subpopulations, which depends on the specific process of inactivation. It is the multi-valued dependence of the cross link density on the control parameter, i. Read More

It has been found that contrarian oscillators usually take a negative role in the collective behaviors formed by conformist oscillators. However, experiments revealed that it is also possible to achieve a strong coherence even when there are contrarians in the system such as neuron networks with both excitable and inhibitory neurons. To understand the underlying mechanism of this abnormal phenomenon, we here consider a complex network of coupled Kuramoto oscillators with mixed positive and negative couplings and present an efficient approach, i. Read More

Through experiments and numerical simulations we explore the behavior of rf SQUID (radio frequency superconducting quantum interference device) metamaterials, which show extreme tunability and nonlinearity. The emergent electromagnetic properties of this metamaterial are sensitive to the degree of coherent response of the driven interacting SQUIDs. Coherence suffers in the presence of disorder, which is experimentally found to be mainly due to a dc flux gradient. Read More

Efficient bacterial chromosome segregation typically requires the coordinated action of a three-components, ATP-fueled machinery called the partition complex. We present a phenomenological model accounting for the dynamic activity of this system. The model is obtained by coupling simple linear reaction-diffusion equations with a proteophoresis, or "volumetric" chemophoresis, force field. Read More

We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the subsequent spreading, pinning, or retraction of the activations; such analysis enables the characterization of the formation of stationary patterns of localized activity. The results are interpreted with a theoretical analysis of a simplified bistable reaction-diffusion model. Read More

**Authors:**Peter Csermely

Our century has unprecedented new challenges, which need creative solutions and deep thinking. Contemplative, deep thinking became an "endangered species" in our rushing world of Tweets, elevator pitches and fast decisions. Here we describe that important aspects of both creativity and deep thinking can be understood as network phenomena of conceptual and social networks. Read More

We consider a system of nonlinear partial differential equations that describes an age-structured population inhabiting several temporally varying patches. We prove existence and uniqueness of solution and analyze its large-time behavior in cases when the environment is constant and when it changes periodically. A pivotal assumption is that individuals can disperse and that each patch can be reached from every other patch, directly or through several intermediary patches. Read More

We investigate the influence of time-delayed coupling in a ring network of non-locally coupled Stuart-Landau oscillators upon chimera states, i.e., space-time patterns with coexisting partially coherent and partially incoherent domains. Read More

Understanding the dynamical behavior of complex systems is of exceptional relevance in everyday life, from biology to economy. In order to describe the dynamical organization of complex systems, existing methods require the knowledge of the network topology. By contrast, in this thesis we develop a new method based on Information Theory which does not require any topological knowledge. Read More

This work aimed, to determine the characteristics of activity series from fractal geometry concepts application, in addition to evaluate the possibility of identifying individuals with fibromyalgia. Activity level data were collected from 27 healthy subjects and 27 fibromyalgia patients, with the use of clock-like devices equipped with accelerometers, for about four weeks, all day long. The activity series were evaluated through fractal and multifractal methods. Read More

In this work we have systematically studied the dynamical phase transitions in the Kuramoto-Sakaguchi model of synchronizing phase oscillators controlled by disorder in the Sakaguchi phases. We find out the steady state phase diagrams for quenched and annealed kinds of disorder in the Sakaguchi parameters using the conventional order parameter and other statistical quantities like strength of incoherence and discontinuity measures. We have shown that the Sakaguchi phase factor has a manifestation as a disordering field in this system. Read More

Multidimensional systems coupled via complex networks are widespread in nature and thus frequently invoked for a large plethora of interesting applications. From ecology to physics, individual entities in mutual interactions are grouped in families, homogeneous in kind. These latter interact selectively, through a sequence of self-consistently regulated steps, whose deeply rooted architecture is stored in the assigned matrix of connections. Read More

Computer experiments that mirror the evolutionary dynamics of sexual and asexual organisms as they occur in nature, tested features proposed to explain the evolution of sexual recombination. Results show that this evolution is better described as a network of interactions between possible sexual forms, including diploidy, thelytoky, facultative sex, assortation, bisexuality, and division of labor between the sexes, rather than a simple transition from parthenogenesis to sexual recombination. Diploidy showed to be fundamental for the evolution of sex; bisexual reproduction emerged only among anisogamic diploids with a synergistic division of reproductive labor; and facultative sex was more likely to evolve among haploids practicing assortative mating. Read More

Spatially distributed limited-cycle oscillators are seen in various physical and biological systems. In internal organs, mechanical motions are induced by the stimuli of spatially distributed limit-cycle oscillators. We study several mechanical motions by limit-cycle oscillators using simple model equations. Read More

Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or dynamical modules. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network: the Modularization of Dynamics Theorem. Read More

Sensory mechanisms in biology, from cells to humans, have the property of adaptivity, whereby the response produced by the sensor is adapted to the overall amplitude of the signal; reducing the sensitivity in the presence of strong stimulus, while increasing it when it is weak. This property is inherently energy consuming and a manifestation of the non-equilibrium nature of living organisms. We explore here how adaptivity affects the effective forces that organisms feel due to others in the context of a uniform swarm, both in two and three dimensions. Read More

Many biological and cognitive systems do not operate deep into one or other regime of activity. Instead, they exploit critical surfaces poised at transitions in their parameter space. The pervasiveness of criticality in natural systems suggests that there may be general principles inducing this behaviour. Read More

Power system dynamic state estimation is essential to monitoring and controlling power system stability. Kalman filtering approaches are predominant in estimation of synchronous machine dynamic states (i.e. Read More

**Authors:**Tomislav Stankovski

Interactions in nature can be described by their coupling strength, direction of coupling and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems, however there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here { synchronization transition occurs only due to the time-variability of the coupling functions, while the net coupling strength is constant throughout the observation time. Read More

In this paper we focus on the construction of numerical schemes for nonlinear Fokker-Planck equations that preserve the structural properties, like non negativity of the solution, entropy dissipation and large time behavior. The methods here developed are second order accurate, they do not require any restriction on the mesh size and are capable to capture the asymptotic steady states with arbitrary accuracy. These properties are essential for a correct description of the underlying physical problem. Read More