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

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

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

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

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

Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. If multiple such networks are coupled together, the question arises whether these rhythms will synchronize. We investigate the impact of noise on this synchronization for strong inhibitory pulse-coupling and find that increasing the noise can synchronize the population rhythms, even if the noisy inputs to different oscillators are completely uncorrelated. Read More

An avalanche or cascade occurs when one event causes one or more subsequent events, which in turn may cause further events in a chain reaction. Avalanching dynamics are studied in many disciplines, with a recent focus on average avalanche shapes, i.e. Read More

Revealing how a biological network is organized to realize its function is one of the main topics in systems biology. The functional backbone network, defined as the primary structure of the biological network, is of great importance in maintaining the main function of the biological network. We propose a new algorithm, the tinker algorithm, to determine this core structure and apply it in the cell-cycle system. Read More

Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far reaching applications in many domains, including engineering and medicine. In this paper, we formulate the synchronization control in dynamical systems as an optimization problem and present a multi-objective genetic programming-based approach to infer optimal control functions that drive the system from a synchronized to a non-synchronized state and vice-versa. Read More

We study the collective dynamics of a lattice model of stochastically interacting agents with a weighted field of vision. We assume that agents preferentially interact with neighbours, depending on their relative location, through velocity alignments and the additional constraint of exclusion. Unlike in previous models of flocking, here the stochasticity arises intrinsically from the interactions between agents, and its strength is dependent on the local density of agents. Read More

The effect of laziness in the group chase and escape problem is studied using a simple model. The laziness is introduced as random walks in two ways: uniformly and in a "division of labor" way. It is shown that, while the former is always ineffective, the latter can improve the efficiency of catching, through the formation of pincer attack configuration by diligent and lazy chasers. Read More

**Affiliations:**

^{1}COFFEE, UCA,

^{2}COFFEE, UCA,

^{3}IMFT,

^{4}MAPMO

We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic arguments. Hence, we are interested in the simulation of approached models that contain stiff terms and large speeds of propagation. Read More

Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these relations by incorporating sampling-based measures of the transient behaviour of the system, its survivability, as well as its asymptotic behaviour, its basin stability. By combining basin stability and survivability we uncover novel, previously unknown asymptotic states with solitary, desynchronized oscillators which are rotating with a frequency different from their natural one. Read More

Pattern formation by injected fluid induced by a coupling of solidification and hydrodynamics was analyzed. An experimental system was constructed where an aqueous solution of cobalt chloride was injected into a cell filled with sodium silicate solution. The reaction of these two solutions resulted in the formation of silica gel, i. Read More

The stability of powergrid is crucial since its disruption affects systems ranging from street lightings to hospital life-support systems. Nevertheless, large blackouts are inevitable if powergrids are in the state of self-organized criticality (SOC). In this paper, we introduce a simple model of evolving powergrid and establish its connection with the sandpile model, i. Read More

Today's colleges and universities consist of highly complex structures that dictate interactions between the administration, faculty, and student body. These structures can play a role in dictating the efficiency of policy enacted by the administration and determine the effect that curriculum changes in one department have on other departments. Despite the fact that the features of these complex structures have a strong impact on the institutions, they remain by-and-large unknown in many cases. Read More

While the statistical and resilience properties of the Internet are no more changing significantly across time, the Darknet, a network devoted to keep anonymous its traffic, still experiences rapid changes to improve the security of its users. Here, we study the structure of the Darknet and we find that its topology is rather peculiar, being characterized by non-homogenous distribution of connections -- typical of scale-free networks --, very short path lengths and high clustering -- typical of small-world networks -- and lack of a core of highly connected nodes. We propose a model to reproduce such features, demonstrating that the mechanisms used to improve cyber-security are responsible for the observed topology. Read More

Gene expression is a noisy process that leads to regime shift between alternative steady states among individual living cells, inducing phenotypic variability. The effects of white noise on the regime shift in bistable systems have been well characterized, however little is known about such effects of colored noise (noise with non-zero correlation time). Here, we show that noise correlation time, by considering a genetic circuit of autoactivation, can have significant effect on the regime shift in gene expression. Read More

Compartments are ubiquitous throughout biology, yet their importance stretches back to the origin of cells. In the context of origin of life, we assume that a protocell, a compartment enclosing functional components, requires $N$ components to be evolvable. We take interest in the timescale in which a minimal evolvable protocell is produced. Read More

We study under which conditions systems of coupled oscillators on complex networks display remote synchronization, a situation where pairs of vertices, not necessarily physically linked, but with the same network symmetry, are synchronized. Read More

In this paper, we develop an agent-based version of the Diamond search equilibrium model - also called Coconut Model. In this model, agents are faced with production decisions that have to be evaluated based on their expectations about the future utility of the produced entity which in turn depends on the global production level via a trading mechanism. While the original dynamical systems formulation assumes an infinite number of homogeneously adapting agents obeying strong rationality conditions, the agent-based setting allows to discuss the effects of heterogeneous and adaptive expectations and enables the analysis of non-equilibrium trajectories. Read More

We consider a variation of the Kuramoto model with dynamic coupling, where the coupling strengths are allowed to evolve in response to the phase difference between the oscillators, a model first considered by Ha, Noh and Park. In particular we study the stability of fixed points for this model. We demonstrate a somewhat surprising fact: namely that the fixed points of this model, as well as their stability, can be completely expressed in terms of the fixed points and stability of the analogous classical Kuramoto problem where the coupling strengths are fixed to a constant (the same for all edges). Read More

The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and their phases need to appoximately lock to guarantee a steady power flow. Here, we analyze the existence and multitude of such phase-locked states. Read More

We study the dynamics of a swarm in which agents have full knowledge of the physical laws governing the system they live in. Agents aim to maximize their resource uptake by solving these laws to predict the future of their environment and other agents. The agents also take into account the effects of their and other agents' actions on the environment, which in some cases cause their predictive solutions to not converge. Read More

Ancient and medieval harbours connected via navigable and terrestrial routes could be interpreted as elements of complex traffic networks. Based on evidence from three projects in Priority Programme 1630 (Fossa Carolina, Inland harbours in Central Europe and Byzantine harbours on the Balkan coasts) we present a pioneer study to apply concepts and tools of network theory on archaeological and on written evidence as well as to integrate this data into different network models. Our diachronic approach allows for an analysis of the temporal and spatial dynamics of webs of connectivity with a focus on the 1st millennium AD. Read More

The emergence of cosmic structure is commonly considered one of the most complex phenomena in Nature. However, this complexity has never been defined nor measured in a quantitative and objective way. In this work we propose a method to measure the information content of cosmic structure and to quantify the complexity that emerges from it, based on Information Theory. Read More

Shifting our electricity generation from fossil fuel to renewable energy sources introduces large fluctuations to the power system. Here, we demonstrate how increased fluctuations, reduced damping and reduced intertia may undermine the dynamical robustness of power grid networks. Focusing on fundamental noise models, we derive analytic insights into which factors limit the dynamic robustness and how fluctuations may induce a system escape from an operating state. Read More

Feed-in fluctuations induced by renewables are one of the key challenges to the stability and quality of electrical power grids. In particular short-term fluctuations disturb the system on a time scale, on which load balancing does not operate yet and the system is intrinsically governed by self-organized synchronization. Wind and solar power are known to be strongly non-Gaussian with intermittent increment statistics in these time scales. Read More

The ability of a honeybee swarm to select the best nest site plays a fundamental role in determining the future colony's fitness. To date, the nest-site selection process has mostly been modelled and theoretically analysed for the case of binary decisions. However, when the number of alternative nests is larger than two, the decision process dynamics qualitatively change. Read More

We study numerically the oscillation death state in the phase oscillator model proposed byWinfree. We found that the phases in this state follow very simple rules, actually, besides intrinsic properties of the oscillators, such as natural frequency and pulse shape, they depend only on the inverse of the degree. Other topological properties such as transitivity or associativity seems to play no role on this state. Read More

Collective social events operate at many levels of organization -- from individuals to crowds -- presenting a variety of temporal and spatial scales of activity, whose causal interactions challenge our understanding of social systems. Large data sets of social media activity provide an unprecedented opportunity to investigate the processes that govern the coordination within and between those scales. Using as a case study a data set comprising 1. Read More

Global, population-wide oscillations in models of cyclic dominance may result in the collapse of biodiversity due to the accidental extinction of one species in the loop. Previous research has shown that such oscillations can emerge if the interaction network has small-world properties, and more generally, because of long-range interactions among individuals or because of mobility. But although these features are all common in nature, global oscillations are rarely observed in actual biological systems. Read More

Location-based social media make it possible to understand social and geographic aspects of human activities. However, previous studies have mostly examined these two aspects separately without looking at how they are linked. The study aims to connect two aspects by investigating whether there is any correlation between social connections and users' check-in locations from a socio-geographic perspective. Read More

Many networks are used to transfer information or goods, in other words, they are navigated. The larger the network, the more difficult it is to navigate efficiently. Indeed, information routing in the Internet faces serious scalability problems due to its rapid growth, recently accelerated by the rise of the Internet of Things. Read More