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In this work we present a model for the propagation of culture on networks of different topology and by considering different underlying dynamics. We extend a previous model proposed by Axelrod by letting a majority govern the dynamics of changes.
We describe a form of memory exhibited by extended excitable systems driven by stochastic fluctuations. Under such conditions, the system self-organizes into a state characterized by power-law correlations thus retaining long-term memory of previous states.
When two systems are coupled, one can play the role of the driver, and the other can be the driven or response system. In this scenario, the driver system can behave as an external forcing.
Non-linear oscillator networks have revealed properties as the remote synchronization and the quorum sensing. The remote synchronization, defined as the synchronization of nodes not directly connected by any sequence of synchronized nodes, was found firstly in networks of amplitude oscillators and recently in bipartit...
The Hopfield-Tank (1985) recurrent neural network architecture for the Traveling Salesman Problem is generalized to a fully interconnected "cellular" neural network of regular oscillators. Tours are defined by synchronization patterns, allowing the simultaneous representation of all cyclic permutations of a gi...
In this work we comment some conclusions derived from the analysis of recent proposals on the field of chaos-based cryptography. These observations remark the main problems detected in some of those schemes under examination.
In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all these systems present stochastic oscillations hovering around the critical region...
Mortgage prepayments play a crucial role in the pricing and hedging of mortgage backed securities. An important feature of mortgage prepayment modeling is burnout; as time goes on those borrowers who have the greatest tendency to refinance are removed from the pool leaving only those that are less likely to refinance....
We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow universal Gaussian orthogonal ensemble statistics of random matrix theory.
We introduce and study a dynamic transport model exhibiting Self-Organized Criticality. The novel concepts of our model are the probabilistic propagation of activity and unbiased random repartition of energy among the active site and its nearest neighbors.
We show that the way in which the Shannon entropy of sequences produced by an information source converges to the source's entropy rate can be used to monitor how an intelligent agent builds and effectively uses a predictive model of its environment. We introduce natural measures of the environment's apparent ...
This paper investigates applicability of thermodynamic concepts and principles to competitive systems. We show that Tsallis entropies are suitable for characterisation of systems with transitive competition when mutations deviate from Gibbs mutations.
A notion of delegated causality is introduced. This subtle kind of causality is dual to interventional causality.
Up to now both information and its connection to reality have not scientifically conclusive definitions neither implicit origin. They emerge in observing multiple impulses interactive yes-no actions modeling information Bits.
We make a short review about the synchronization in coupled phase oscillator models. Next, we study the common-noise-induced synchronization among active rotators.
We propose a model with heterogeneous interacting traders which can explain some of the stylized facts of stock market returns. In the model synchronization effects, which generate large fluctuations in returns, can arise either from an aggregate exogenous shock or, even in its absence, purely from communication and i...
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature.
By generalizing the measurements on the game experiments of mixed strategy Nash equilibrium, we study the dynamical pattern in a representative dynamic stochastic general equilibrium (DSGE). The DSGE model describes the entanglements of the three variables (output gap [$y$], inflation [$\pi$] and nominal interest rate...
We investigate the role of the learning rate in a Kuramoto Model of coupled phase oscillators in which the coupling coefficients dynamically vary according to a Hebbian learning rule. According to the Hebbian theory, a synapse between two neurons is strengthened if they are simultaneously co-active.
The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy's Law. We consider flows in both Lagrangian and Eulerian formulations.
Optimal entrainment of a quantum nonlinear oscillator to a periodically modulated weak harmonic drive is studied in the semiclassical regime. By using the semiclassical phase reduction theory recently developed for quantum nonlinear oscillators, two types of optimization problems, one for the stability and the other f...
Controlling rhythmic systems, typically modeled as limit-cycle oscillators, is an important subject in real-world problems. Phase reduction theory, which simplifies the multidimensional oscillator state under weak input to a single phase variable, is useful for analyzing the oscillator dynamics.
Maintaining a competitive edge requires a firm to replace deteriorating business lines with new projects. Accordingly, part of a firm's value resides in its ability to exploit new opportunities.
We have examined the synchronization and de-synchronization transitions observable in the Kuramoto model with a standard pair-wise first harmonic interaction plus a higher order (triadic) symmetric interaction for unimodal and bimodal Gaussian distributions of the natural frequencies $\{ \omega_i \}$. These transition...
Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible in network-organized systems, such as cellular networks in morphogenesis and eco...
We study a large population of globally coupled phase oscillators subject to common white Gaussian noise and find analytically that the critical coupling strength between oscillators for synchronization transition decreases with an increase in the intensity of common noise. Thus, common noise promotes the onset of syn...
The excitable behaviour is considered as motion of a particle in a potential field in the presence of dissipation. The dynamics of the oscillator proposed in the present paper corresponds to the excitable behaviour in a potential well under condition of positive dissipation.
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.
Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity dependent synaptic plasticity.
We show that an introduction of a phase parameter ($\alpha$), with $0 \le \alpha \le \pi/2$, in the interlayer coupling terms of multiplex networks of Kuramoto oscillators can induce explosive synchronization (ES) in the multiplexed layers. Along with the {\alpha} values, the hysteresis width is determined by the inte...
Complex systems are challenging to control because the system responds to the controller in a nonlinear fashion, often incorporating feedback mechanisms. Interdependence of systems poses additional difficulties, as cross-system connections enable malicious activity to spread between layers, increasing systemic risk.
After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically serves to drive disorder, increasing the stability of the incoherent state.
A mystery surrounds the stability properties of the splay-phase periodic solutions to a series array of N Josephson junction oscillators. Contrary to what one would expect from dynamical systems theory, the splay state appears to be neutrally stable for a wide range of system parameters.
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.
We investigate dynamical properties of traffic flow using the stochastic car-following model with modified optimal velocity on circular road. The safety distance following the two-second rule and autonomous vehicles, acting as agents, obeying simple requirements are incorporated into the model.
In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be regulated by substituting time delays by phase shifts at constant collective fre...
The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not necessarily mean that the system exhibits self-organized criticality.
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear ampli...
With the advent of inexpensive simple humanoid robots, new classes of robotic questions can be considered experimentally. One of these is collective behavior of groups of humanoid robots, and in particular robot synchronization and swarming.
Chimera states, states of coexistence of synchronous and asynchronous motion, have been a subject of extensive research since they were first given a name in 2004. Increased interest has lead to their discovery in ever new settings, both theoretical and experimental.
In this paper, we continue the discussion on database classifiers constructed with networks of interacting chemical oscillators. In our previous papers we demonstrated that a small, regular network of oscillators can predict if three random numbers in the range $[0,1]$ describe a point located inside a sphere inscribe...
For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via bifurcations. The coupling is modeled using the phase-response-curve (PRC), which measure...
A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining in...
Neurons regulate the distribution of signaling components across an extended tree-like cellular structure using both local and global feedback control. This is hypothesized to allow homeostatic control of the electrical activity of a neuron and at the same time enable normalization of distribution of inputs received f...
The phase sensitivity curve or phase response curve (PRC) quantifies the oscillator's reaction to stimulation at a specific phase and is a primary characteristic of a self-sustained oscillatory unit. Knowledge of this curve yields a phase dynamics description of the oscillator for arbitrary weak forcing.
Animal locomotion employs different periodic patterns known as animal gaits. In 1993 Collins and Stewart achieved the characterization in quadrupeds and bipeds by using permutation symmetries groups which impose constrains in the locomotion centre called Central Generator Pattern (CGP) in the animal brain.
We study an evolutionary version of the Prisoner's Dilemma game, played by agents placed in a small-world network. Agents are able to change their strategy, imitating that of the most successful neighbor.
We study a simple two-dimensional swarmalator model that incorporates higher-order phase interactions, uncovering a diverse range of collective states. The latter include spatially coherent and gas-like configurations, neither of which appear in models with only pairwise interactions.
Dengue viral infections show unique infection patterns arising from its four serot- ypes, (DENV-1,2,3,4). Its effects range from simple fever in primary infections to potentially fatal secondary infections.
In this paper, we propose a kinetic model of traffic flow with uncertain binary interactions, which explains the scattering of the fundamental diagram in terms of the macroscopic variability of aggregate quantities, such as the mean speed and the flux of the vehicles, produced by the microscopic uncertainty. Moreover,...
Linear response theory, the backbone of non-equilibrium statistical physics, has recently been extended to explain how and why non-ergodic renewal processes are insensitive to simple perturbations, such as in habituation. It was established that a permanent correlation resulted between an external stimulus and the res...
Synchronization with noise is important for understanding biophysical processes at nano- and micro-meter scales, such as neuronal firing and flagellar rotations. To understand the energetics of these processes, stochastic thermodynamics approaches are useful.
The "social-networking revolution" of late (e.g., with the advent of social media, Facebook, and the like) has been propelling the crusade to elucidate the embedded networks that underlie economic activity. An unexampled synthesis of network science and economics uncovers how the web of human interactions spur...
Following extensive numerical experiments, it has been suggested that the evolution of competing computer programs in artificial life simulations shows signs of being a self-organized critical process. The primary evidence for this claim comes from the distribution of the lifetimes of species in the simulations, which...
We investigate the emergence of synchronization in heterogeneous networks of chaotic maps. Our findings reveal that a small cluster of highly connected maps is responsible for triggering the spark of synchronization.
It has been pointed out that if an autocatalytic cycle produces primitive membrane chemicals, it can compose a self-maintaining proto cell. Moreover, it is known that a proto cell can divide itself spontaneously as it grows.
We propose a scenario for the origin of life based on the coevolution of lipid bilayer vesicles and protein channels.
The viral load is known to be a chief predictor of the risk of transmission of infectious diseases. In this work, we investigate the role of the individuals' viral load in the disease transmission by proposing a new susceptible-infectious-recovered epidemic model for the densities and mean viral loads of each comp...
A spacially extended model of the collective behavior of a large number of locally acting organisms is proposed in which organisms move probabilistically between local cells in space, but with weights dependent on local morphogenetic substances, or morphogens. The morphogens are in turn are effected by the passage of ...
Crime is an economically important activity, sometimes called the industry of crime. It may represent a mechanism of wealth distribution but also a social and economic charge because of the cost of the law enforcement system.
We employ the circular cumulant approach to construct a low dimensional description of the macroscopic dynamics of populations of phase oscillators (elements) subject to non-Gaussian white noise. Two-cumulant reduction equations for alpha-stable noises are derived.
We found that a network-organized metapopulation of cooperators, defectors and destructive agents playing the public goods game with mutations, can collectively reach global synchronization or chimera states. Global synchronization is accompanied by a collective periodic burst of cooperation, whereas chimera states re...
Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases.
In this contribution we consider Collective Behaviours as coherent sequences of spatial configurations adopted by interacting agents through corresponding different structures over time. Multiple structures over time and their sequences are considered as Meta-Structures establishing sequences of spatial configurations...
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states.
We analyze the collective dynamics of an ensemble of globally coupled, externally forced, identical mechanical oscillators with cubic nonlinearity. Focus is put on solutions where the ensemble splits into two internally synchronized clusters, as a consequence of the bistability of individual oscillators.
A locally iterative learning (LIL) rule is adapted to a model of the associative memory based on the evolving recurrent-type neural networks composed of growing neurons. There exist extremely different scale parameters of time, the individual learning time and the generation in evolution.
We introduce a method that can be used to evolve the topology of a network in a way that preserves both the network's spectral as well as local structure. This method is quite versatile in the sense that it can be used to evolve a network's topology over any collection of the network's elements.
We investigate the combined effects of distributed delay and the balance between excitatory and inhibitory nodes on the stability of synchronous oscillations in a network of coupled Stuart--Landau oscillators. To this end a network model is proposed for which the stability can be investigated analytically.
We present a general framework for the study of coevolution in dynamical systems. This phenomenon consists of the coexistence of two dynamical processes on networks of interacting elements: node state change and rewiring of links between nodes.
We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a thresho...
We explore the phase reduction in networks of coupled oscillators in the higher orders of the coupling parameter. For coupled Stuart-Landau oscillators, where the phase can be introduced explicitly, we develop an analytic perturbation procedure to allow for the obtaining of the higher-order approximation explicitly.
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., deviations from the limit-cycle attractor, has been intro...
Accurately capturing the nonlinear dynamic behavior of structures remains a significant challenge in mechanics and engineering. Traditional physics-based models and data-driven approaches often struggle to simultaneously ensure model interpretability, noise robustness, and estimation optimality.
Plasmodium of acellular slime mould Physarum polycephalum is a very large eukaryotic microbe visible to the unaided eye. During its foraging behaviour the plasmodium spans sources of nutrients with a network of protoplasmic tubes.
To elucidate the role of environmental conditions in molecular-level dynamics and to study their impact on macroscopic brain tumor growth patterns, the expression of the genes Tenascin C and PCNA in a 2D agent-based model for the migratory trait is calibrated using experimental data from the literature, while the expre...
This paper presents description of time evolution of averages of Markov process in wide range of noise intensity. Exact expression of time scale of average evolution has been obtained.
We study the emergence of a power law distribution in the systems which can be characterized by a hierarchically organized supplying network. It is shown that conservation laws on the branches of the network can, at some approximation, impose power law properties on the systems.
Turing's theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and the mechanisms of pattern selection are well understood in small networks....
We model a close-knit community of friends and enemies as a fully connected network with positive and negative signs on its edges. Theories from social psychology suggest that certain sign patterns are more stable than others.
An important goal for swarming research is to create methods for predicting, controlling and designing swarms, which produce collective dynamics that solve a problem through emergent and stable pattern formation, without the need for constant intervention, and with a minimal number of parameters and controls. One such...
Dynamical effects on healthy brains and brains affected by tumor are investigated via numerical simulations. The brains are modeled as multilayer networks consisting of neuronal oscillators, whose connectivities are extracted from Magnetic Resonance Imaging (MRI) data.
The activity in the brain cortex remarkably shows a simultaneous presence of robust collective oscillations and neuronal avalanches, where intermittent bursts of pseudo-synchronous spiking are interspersed with long periods of quiescence. The mechanisms allowing for such a coexistence are still a matter of an intensiv...
A city is a whole, as are all cities in a country. Within a whole, individual cities possess different degrees of wholeness, defined by Christopher Alexander as a life-giving order or simply a living structure.
Two fundamental issues surrounding research on the image of the city respectively focus on the city's external and internal representations. The external representation in the context of this paper refers to the city itself, external to human minds, while the internal representation concerns how the city is repres...
We consider the synchronization of oscillators in complex networks where there is an interplay between the oscillator dynamics and the network topology. Through a remarkable transformation in parameter space and the introduction of virtual frequencies we show that Kuramoto oscillators on annealed networks, with or wit...
I elaborate on the tension between Luhmann's social systems theory and Habermas' theory of communicative action, and argue that this tension can be resolved by focusing on language as the interhuman medium of the communication which enables us to develop symbolically generalized media of communication such as t...
A model of an evolving network of interacting molecular species is shown to exhibit repeated rounds of crashes in which several species get rapidly depopulated, followed by recoveries. The network inevitably self-organizes into an autocatalytic structure, which consists of an irreducible `core' surrounded by a par...
The definition of a mobilized system and its efficiency are introduced. The existence of an optimal (maximally efficient) system is proved by an application of Young measures and compensated compactness.
The unprecedented access offered by the World Wide Web brings with it the potential to gather huge amounts of data on human activities. Here we exploit this by using a toy model of financial markets, the Minority Game (MG), to investigate human speculative trading behaviour and information capacity.
A binary game is introduced and analysed. N players have to choose one of the two sides independently and those on the minority side win.
Purpose: In the tradition of Spencer Brown's (1969) Laws of Form, observation was defined in Luhmann's (1984) social systems theory as the designation of a distinction. In the sociological design, however, the designation specifies only a category for the observation.
In this paper, we address the reduced-order synchronization problem between two chaotic memristive Hindmarsh-Rose (HR) neurons of different orders using two distinct methods. The first method employs the Lyapunov active control technique.
The synchronization analysis of limit-cycle oscillators is prevalent in many fields, including physics, chemistry, and life sciences. It relies on the phase calculation that utilizes measurements.
We discuss the appearance of oscillatory and standing wave states in second-order oscillator networks showing that it is a special case of a more general mechanism involving secondary synchronized clusters induced by inertia. Using a time-periodic mean-field ansatz, we find a bistable mechanism involving a stable fixe...
Significant radar range degradation can be incurred due to variations in antenna impedance from changing array scan angle. Element-wise reconfigurable impedance tuners can be used to optimally match the power amplifier device; however, the impedance matching can also affect the array pattern.
This presentation's Part 3 studies the evolutionary information processes and regularities of evolution dynamics, evaluated by an entropy functional (EF) of a random field (modeled by a diffusion information process) and an informational path functional (IPF) on trajectories of the related dynamic process (Lerner 2...
The Deep Time-Delay Reservoir Computing concept utilizes unidirectionally connected systems with time-delays for supervised learning. We present how the dynamical properties of a deep Ikeda-based reservoir are related to its memory capacity (MC) and how that can be used for optimization.
We present a fixed energy sandpile (FES) model which, by increasing the initial energy,undergoes, at the level of individual configurations, a discontinuous <a href="http://transition.The" rel="external noopener nofollow" class="link-external link-http">this http URL</a> model is obtained by modifying the toppling proc...
The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplings.

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