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

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

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

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, testing features proposed to explain the evolution of sexual recombination, 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, rather than a simple transition from parthenogenesis to sexual recombination. Results show that sex is an adaptation to manage genetic complexity in evolution; that bisexual reproduction emerges only among anisogamic diploids with a synergistic division of reproductive labor; and that facultative sex is more likely to evolve among haploids practicing assortative mating. Looking at the evolution of sex as a complex system explains better the diversity of sexual strategies known to exist in nature. 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

We consider evolving networks in which each node can have various associated properties (a state) in addition to those that arise from network structure. For example, each node can have a spatial location and a velocity, or some more abstract internal property that describes something like social trait. Edges between nodes are created and destroyed, and new nodes enter the system. Read More

This note presents a minimal approach to the origin of life, following standard ideas. We pay special attention to the point of view of non-equilibrium statistical mechanics, and in particular to detailed balance. As a consequence we propose a characterization of pre-biological states. Read More

The question of why and how animal and human groups form temporarily stable hierarchical organizations has long been a great challenge from the point of quantitative interpretations. The prevailing observation/consensus is that a hierarchical social or technological structure is optimal considering a variety of aspects. Here we introduce a simple quantitative interpretation of this situation using an approach reminiscent of those developed for describing complex behaviour in terms of statistical mechanics. Read More

We show the existence of chimera-like states in two distinct groups of identical populations of globally coupled Stuart-Landau oscillators. The existence of chimera-like states occurs only for a small range of frequency difference between the two populations and these states disappear for an increase of mismatch between the frequencies. Here the chimera-like states are characterized by the synchronized oscillations in one population and desynchronized oscillations in another population. Read More

We numerically study jamming transitions in pedestrian flow interacting with an attraction, mostly based on the social force model for pedestrians who can join the attraction. We formulate the joining probability as a function of social influence from others, reflecting that individual choice behavior is likely influenced by others. By controlling pedestrian influx and the social influence parameter, we identify various pedestrian flow patterns. Read More

We analyze repulsively coupled Kuramoto oscillators, which are exposed to a distribution of natural frequencies. This source of disorder leads to closed orbits with a variety of different periods, which can be orders of magnitude longer than periods of individual oscillators. By construction the attractor space is quite rich. Read More

While interdependent systems have usually been associated with increased fragility, we show that strengthening the interdependence between dynamical processes on different networks can make them more robust. By coupling the dynamics of networks that in isolation exhibit catastrophic collapse with extinction of nodal activity, we demonstrate system-wide persistence of activity for an optimal range of interdependence between the networks. This is related to the appearance of attractors of the global dynamics comprising disjoint sets ("islands") of stable activity. Read More

Network structure can have significant effects on the propagation of diseases, memes, and information on social networks. Such effects depend on the specific type of dynamical process that affects the nodes and edges of a network, and it is important to develop tractable models of spreading processes on networks to explore how network structure affects dynamics. In this paper, we incorporate the idea of \emph{synergy} into a two-state ("active" or "passive") threshold model of social influence on networks. Read More

During embryo development, patterns of protein concentration appear in response to morphogen gradients. The archetypal pattern is the French flag composed of three chemically-distinct zones separated by sharp borders. Chemical concentration serves the underlying cells both as an indicator of location and as a fate selector. Read More

In recent years, we have observed a significant trend towards filling the gap between social network analysis and control. This trend was enabled by the introduction of new mathematical models describing dynamics of social groups, the advancement in complex networks theory and multi-agent systems, and the development of modern computational tools for big data analysis. The aim of this tutorial is to highlight a novel chapter of control theory, dealing with applications to social systems, to the attention of the broad research community. Read More

It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' escape time gives an expression for the mean escape time in the asymptotic limit. If a number of multistable systems are coupled into a network structure, a transition at one site may change the transition properties at other sites. Read More

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states. Read More

Phase reduction framework for limit-cycling systems based on isochrons has been used as a powerful tool for analyzing rhythmic phenomena. Recently, the notion of isostables, which complements the isochrons by characterizing amplitudes of the system state, i.e. Read More

Recent remarkable progress in wave-front shaping has enabled control of light propagation inside linear media to focus and image through scattering objects. In particular, light propagation in multimode fibers comprises complex intermodal interactions and rich spatiotemporal dynamics. Control of physical phenomena in multimode fibers and their application are in its infancy, opening opportunities to take advantage of the complex mode interactions. Read More

The mathematical framework of multiplex networks has been increasingly realized as a more suitable framework for modelling real-world complex systems. In this work, we investigate the optimization of synchronizability in multiplex networks by evolving only one layer while keeping other layers fixed. Our main finding is to show the conditions under which the efficiency of convergence to the most optimal structure is almost as good as the case where both layers are rewired during an optimization process. Read More

**Affiliations:**

^{1}Michigan State University,

^{2}Michigan State University,

^{3}Michigan State University,

^{4}Michigan State University

While all organisms on Earth descend from a common ancestor, there is no consensus on whether the origin of this ancestral self-replicator was a one-off event or whether it was only the final survivor of multiple origins. Here we use the digital evolution system Avida to study the origin of self-replicating computer programs. By using a computational system, we avoid many of the uncertainties inherent in any biochemical system of self-replicators (while running the risk of ignoring a fundamental aspect of biochemistry). Read More

The model of a double-well oscillator with nonlinear dissipation is studied. The self-sustained oscillations regime and the excitable one are described. The first regime consists in the coexistence of two stable limit cycles in the phase space, which correspond to the self-sustained oscillations of the point mass in either potential well. Read More

Network science is increasingly being developed to get new insights about behavior and properties of complex systems represented in terms of nodes and interactions. One useful approach is investigating localization properties of eigenvectors which have diverse applications ranging from detection of influential nodes to disease-spreading phenomena in underlying networks. In this work, we evolve an initial random network with an edge rewiring optimization technique considering the inverse participation ratio as a fitness function to obtain a network having a localized principle eigenvector and analyze various properties of the optimized networks. Read More

We study how large functional networks can grow stably under possible cascading overload failures and evaluated the maximum stable network size above which even a small-scale failure would cause a fatal breakdown of the network. Employing a model of cascading failures induced by temporally fluctuating loads, the maximum stable size $n_{\text{max}}$ has been calculated as a function of the load reduction parameter $r$ that characterizes how quickly the total load is reduced during the cascade. If we reduce the total load sufficiently fast ($r\ge r_{\text{c}}$), the network can grow infinitely. Read More

The synchronized magnetization dynamics in ferromagnets on a nonmagnetic heavy metal caused by the spin Hall effect is investigated theoretically. The direct and inverse spin Hall effects near the ferromagnetic/nonmagnetic interface generates longitudinal and transverse electric currents. The phenomenon is known as the spin Hall magnetoresistance effect, whose magnitude depends on the magnetization direction in the ferromagnet due to the spin transfer effect. Read More

Collective behaviors of populations of coupled oscillators have attracted much attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynam- ical mechanism of collective synchronizations by adopting the star-topology of coupled oscillators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe-Strogatz transformation, Ott-Antonsen ansatz, and the ensemble order parameter approach. Read More

Ionic liquids are solvent-free electrolytes, some of which possess an intriguing self-assembly property. Using a mean-field framework (based on Onsager's relations) we show that bulk nano-structures arise via type-I and II phase transitions (PT), which directly affect the electrical double layer (EDL) structure. Ginzburg-Landau equation is derived and PT are related to temperature, potential and interactions. Read More

In the social, behavioral, and economic sciences, it is an important problem to predict which individual opinions will eventually dominate in a large population, if there will be a consensus, and how long it takes a consensus to form. This idea has been studied heavily both in physics and in other disciplines, and the answer depends strongly on both the model for opinions and for the network structure on which the opinions evolve. One model that was created to study consensus formation quantitatively is the Deffuant model, in which the opinion distribution of a population evolves via sequential random pairwise encounters. Read More

We study the stochastic dynamics of strongly-coupled excitable elements on a tree network. The peripheral nodes receive independent random inputs which may induce large spiking events propagating through the branches of the tree and leading to global coherent oscillations in the network. This scenario may be relevant to action potential generation in certain sensory neurons, which possess myelinated distal dendritic tree-like arbors with excitable nodes of Ranvier at peripheral and branching nodes and exhibit noisy periodic sequences of action potentials. Read More

Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level coexists with regular oscillations at the global level is still unclear. Here we show that a combination of stochastic recurrence-based initiation with deterministic refractoriness in an excitable network can reconcile these two features, leading to maximum collective coherence for an intermediate noise level. Read More

A characteristic property of networks is their ability to propagate influences, such as infectious diseases, behavioral changes, and failures. An especially important class of such contagious dynamics is that of cascading processes. These processes include, for example, cascading failures in infrastructure systems, extinctions cascades in ecological networks, and information cascades in social systems. Read More

We discuss synchronization patterns in networks of FitzHugh-Nagumo and Leaky Integrate-and-Fire oscillators coupled in a two-dimensional toroidal geometry. Common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. Read More

We present two different approaches to model power grids as interconnected networks of networks. Both models are derived from a model for spatially embedded mono-layer networks and are generalised to handle an arbitrary number of network layers. The two approaches are distinguished by their use case. Read More

Game theory research on the snowdrift game has showed that gradual evolution of the continuously varying level of cooperation in joint enterprises can demonstrate evolutionary merging as well as evolutionary branching. However, little is known about the consequences of changes in diversity at the cooperation level. In the present study I consider effects of costly rewards on the continuous snowdrift game. Read More

An array of excitable Josephson junctions under global mean-field interaction and a common periodic forcing shows emergence of two important classes of coherent dynamics, librational and rotational motion in the weaker and stronger coupling limits, respectively, with transitions to chimeralike states and clustered states in the intermediate coupling range. In this numerical study, we use the Kuramoto complex order parameter and introduce two measures, a libration index and a clustering index to characterize the dynamical regimes and their transition and locate them in a parameter plane. Read More

For the first time the electrohydrodynamic convection (EHC) of nematic liquid crystals is studied via fully nonlinear simulation. As a system of rich pattern-formation the EHC is mostly studied with negative nematic liquid crystals experimentally, and sometimes with the help of theoretical instability analysis in the linear regime. Up to now there is only weakly nonlinear simulation for a step beyond the emergence of steady convection rolls. Read More

A central result that arose in applying information theory to the stochastic thermodynamics of nonlinear dynamical systems is the Information-Processing Second Law (IPSL): the physical entropy of the universe can decrease if compensated by the Shannon-Kolmogorov-Sinai entropy change of appropriate information-carrying degrees of freedom. In particular, the asymptotic-rate IPSL precisely delineates the thermodynamic functioning of autonomous Maxwellian demons and information engines. How do these systems begin to function as engines, Landauer erasers, and error correctors? Here, we identify a minimal, inescapable transient dissipation engendered by physical information processing not captured by asymptotic rates, but critical to adaptive thermodynamic processes such as found in biological systems. Read More

We revisit the problem of deriving the mean-field values of avalanche critical exponents in systems with absorbing states. These are well-known to coincide with those of an un-biased branching process. Here, we show that for at least 4 different universality classes (directed percolation, dynamical percolation, the voter model or compact directed percolation class, and the Manna class of stochastic sandpiles) this common result can be obtained by mapping the corresponding Langevin equations describing each of these classes into a random walker confined close to the origin by a logarithmic potential. Read More

We investigate the scaling properties of the order parameter and the largest nonvanishing Lyapunov exponent for the fully locked state in the Kuramoto model with a finite number $N$ of oscillators. We show that, for any finite value of $N$, both quantities scale as $(K-K_L)^{1/2}$ with the coupling strength $K$ sufficiently close to the locking threshold $K_L$. We confirm numerically these predictions for oscillator frequencies evenly spaced in the interval $[-1, 1]$ and additionally find that the coupling range $\delta K$ over which this scaling is valid shrinks like $\delta K \sim N^{-\alpha}$ with $\alpha\approx1. Read More