arXiv subjects

Bulcsú Sándor

Publications and source records attributed to Bulcsú Sándor.

18 recordsLinked to original sources

arXiv2026

Maximally chaotic competition for attention in the cultural domain

Memory is a key determinant when cultural items compete for attention and, consequently, for success, as in the case of songs on a music chart. For modeling, one adds memory to Lotka-Volterra models, the reference for Markovian competitive processes. Here we treat memory in terms of an exponential moving average, finding that it leads to an extended region of winnerless chaos characterized by log-normal popularity statistics in trailing top-k charts. Importantly, the observed log-normal behavior collapses to a power-law distribution when the feedback dynamics is fast on the scale of the charting period. This result is in agreement with the observed statistics of real-world music charts (e.g., Billboard and Spotify). In a chaotic state, the size of the largest Lyapunov exponent is a measure of how unpredictable the system is. We find that the largest Lyapunov exponent varies strongly as a function of parameters in the phase where winnerless chaos is stable. Interestingly, the sets of parameters obtained by comparing simulations with real-world cultural-item dynamics extracted from Google Books and Google Trends, movies, Reddit, Wikipedia, Twitter, and scientific publications, are located close to the points in parameter space where the largest Lyapunov exponent reaches its local maximum, namely, close to the point of maximal unpredictability. This result suggests that cultural competitive processes are maximally chaotic when memory is a key determinant.

nlin.CD↗

arXiv2024

Self-organized attractoring in locomoting animals and robots: an emerging field

Locomotion may be induced on three levels. On a classical level, actuators and limbs follow the sequence of open-loop top-down control signals they receive. Limbs may move alternatively on their own, which implies that interlimb coordination must be mediated either by the body or via decentralized inter-limb signaling. In this case, when embodiment is present, two types of controllers are conceivable for the actuators of the limbs, local pacemaker circuits and control principles based on self-organized embodiment. The latter, self-organized control, is based on limit cycles and chaotic attractors that emerge within the feedback loop composed of controller, body, and environment. For this to happen, the sensorimotor loop must be locally closed, e.g. via propriosensation. Here we review the progress made within the framework of self-organized embodiment, with a particular focus on the concept of attractoring. This concept characterizes situations when sets of attractors combining discrete and continuous spectra are available as motor primitives for higher-order control schemes, such as kick control. In particular, we show that a simple generative principle allows for the robust formulation of self-organized embodiment. Based on the recurrent alternation between measuring the actual status of an actuator and providing a target for the actuator to achieve in the next step, we find that the mechanism leads to compliant locomotion for a range of simulated and real-world robots, which include barrel- and sphere-shaped agents, as well as wheeled and legged robots.

nlin.AO↗

arXiv2024

Measuring dynamical phase transitions in time series

There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the underlying chaotic systems is a notoriously difficult task. Building on prior theoretical studies that focus on the discontinuities at $q=1$ in the order-$q$ Rényi-entropy of the trajectory space, we measure the derivative of the spectrum. We derive within the general context of Markov processes a computationally efficient closed-form expression for this measure. We investigate its properties through well-known dynamical systems exploring its scope and limitations. The proposed mathematical instrument can serve as a predictor of dynamical phase transitions in time series.

nlin.CD↗

arXiv2023

Neural self-organization for muscle-driven robots

We present self-organizing control principles for simulated robots actuated by synthetic muscles. Muscles correspond to linear motors exerting force only when contracting, but not when expanding, with joints being actuated by pairs of antagonistic muscles. Individually, muscles are connected to a controller composed of a single neuron with a dynamical threshold that generates target positions for the respective muscle. A stable limit cycle is generated when the embodied feedback loop is closed, giving rise to regular locomotive patterns. In the absence of direct couplings between neurons, we show that force-mediated intra- and inter-leg couplings between muscles suffice to generate stable gaits.

nlin.AO↗

arXiv2022

Flickering candle flames and their collective behavior

Oscillation and collective behavior of diffusion flames is a fascinating phenomena. Considering candle bundles with different sizes in variable oxygen concentration, the flickering dynamics of the flames are experimentally and theoretically investigated. Trends for the flickering frequency as a function of the candle number in the bundle and oxygen concentration is revealed for various topologies of the candles packing. The collective behavior of the flames as a function of their separation distance is studied by measuring an appropriate synchronization order parameter and trough the common oscillation frequency. In agreement with previous results we find a discontinuous phase transition between an in-phase synchronized state at small separation distance and a counter-phase synchronized state at larger separation distances. A previously used dynamical model is modified in order to accommodate our experimental findings.

physics.pop-ph↗

arXiv2020

Synchronization patterns in rings of time-delayed Kuramoto oscillators

Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling. The linear stability of these states is derived and it is found that the stability maps for the dimensionless equations show a high level of symmetry. The size of the attraction basins is numerically investigated. These sizes are changing periodically over several orders of magnitude as the parameters of the model are varied. Simple heuristic arguments are formulated to understand the changes in the attraction basin sizes and to predict the most probable states when the system is randomly initialized.

nlin.PS↗

arXiv2019

When the goal is to generate a series of activities: A self-organized simulated robot arm

Behavior is characterized by sequences of goal-oriented conducts, such as food uptake, socializing and resting. Classically, one would define for each task a corresponding satisfaction level, with the agent engaging, at a given time, in the activity having the lowest satisfaction level. Alternatively, one may consider that the agent follows the overarching objective to generate sequences of distinct activities. To achieve a balanced distribution of activities would then be the primary goal, and not to master a specific task. In this setting, the agent would show two types of behaviors, task-oriented, and task-searching phases, with the latter interseeding the former. We study the emergence of autonomous task switching for the case of a simulated robot arm. Grasping one of several moving objects corresponds in this setting to a specific activity. Overall, the arm should follow a given object temporarily and then move away, in order to search for a new target and reengage. We show that this behavior can be generated robustly when modeling the arm as an adaptive dynamical system. The dissipation function is in this approach time dependent. The arm is in a dissipative state when searching for a nearby object, dissipating energy on approach. Once close, the dissipation function starts to increase, with the eventual sign change implying that the arm will take up energy and wander off. The resulting explorative state ends when the dissipation function becomes again negative and the arm selects a new target. We believe that our approach may be generalized to generate self-organized sequences of activities in general.

nlin.AO↗

arXiv2019

Chaos in time delay systems, an educational review

The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with it various kinds of chaotic phases. Which are then the possible types of time delays, induced chaotic states, and methods suitable to characterize the resulting dynamics? This review presents an overview of the field that includes an in-depth discussion of the most important results, of the standard numerical approaches and of several novel tests for identifying chaos. Special emphasis is placed on a structured representation that is straightforward to follow. Several educational examples are included in addition as entry points to the rapidly developing field of time delay systems.

nlin.CD↗

arXiv2019

Pattern selection in a ring of Kuramoto oscillators

Emergence of generalized synchronization patterns in a ring of identical and locally coupled Kuramoto-type rotators are investigated by different methods. These approaches offer a useful visual picture for understanding the complexity of the dynamics in the high dimensional state-space of this system. Beside the known stable stationary points novel unstable states are revealed. We find that the prediction of the final stationary state is limited by the presence of such saddle points. This is illustrated by considering and comparing two different attempts for forecasting the final stationary state

nlin.PS↗

arXiv2018

Kick control: using the attracting states arising within the sensorimotor loop of self-organized robots as motor primitives

Self-organized robots may develop attracting states within the sensorimotor loop, that is within the phase space of neural activity, body, and environmental variables. Fixpoints, limit cycles, and chaotic attractors correspond in this setting to a non-moving robot, to directed, and to irregular locomotion respectively. Short higher-order control commands may hence be used to kick the system from one self-organized attractor robustly into the basin of attraction of a different attractor, a concept termed here as kick control. The individual sensorimotor states serve in this context as highly compliant motor primitives. We study different implementations of kick control for the case of simulated and real-world wheeled robots, for which the dynamics of the distinct wheels is generated independently by local feedback loops. The feedback loops are mediated by rate-encoding neurons disposing exclusively of propriosensoric inputs in terms of projections of the actual rotational angle of the wheel. The changes of the neural activity are then transmitted into a rotational motion by a simulated transmission rod akin to the transmission rods used for steam locomotives. We find that the self-organized attractor landscape may be morphed both by higher-level control signals, in the spirit of kick control, and by interacting with the environment. Bumping against a wall destroys the limit cycle corresponding to forward motion, with the consequence that the dynamical variables are then attracted in phase space by the limit cycle corresponding to backward moving. The robot, which does not dispose of any distance or contact sensors, hence reverses direction autonomously.

nlin.AO↗

arXiv2018

Attractor metadynamics in terms of target points in slow-fast systems: adiabatic vs. symmetry protected flow in a recurrent neural network

In dynamical systems with distinct time scales the time evolution in phase space may be influenced strongly by the fixed points of the fast subsystem. Orbits then typically follow these points, performing in addition rapid transitions between distinct branches on the time scale of the fast variables. As the branches guide the dynamics of a system along the manifold of former fixed points, they are considered transiently attracting states and the intermittent transitions between branchescorrespond to state switching within transient-state dynamics. A full characterization of the set of former fixed points, the critical manifold, tends to be difficult in high-dimensional dynamical systems such as large neural networks. Here we point out that an easily computable subset of the critical manifold, the set of target points, can be used as a reference for the investigation of high-dimensional slow-fast systems. The set of target points corresponds in this context to the adiabatic projection of a given orbit to the critical manifold. Applying our framework to a simple recurrent neural network, we find that the scaling relation of the Euclidean distance between the trajectory and its target points with the control parameter of the slow time scale allows to distinguish an adiabatic regime from a state that is effectively independent from target points.

cond-mat.dis-nn↗

arXiv2018

Complex activity patterns generated by short-term synaptic plasticity

Short-term synaptic plasticity (STSP) affects the efficiency of synaptic transmission for persistent presynaptic activities. We consider attractor neural networks, for which the attractors are given, in the absence of STSP, by cell assemblies of excitatory cliques. We show that STSP may transform these attracting states into attractor relics, inducing ongoing transient-state dynamics in terms of sequences of transiently activated cell assemblies, the former attractors. Subsequent cell assemblies may be both disjoint or partially overlapping. It may hence be possible to use the resulting dynamics for the generation of motor control sequences.

q-bio.NC↗

arXiv2018

Closed-loop robots driven by short-term synaptic plasticity: Emergent explorative vs. limit-cycle locomotion

We examine the hypothesis, that short-term synaptic plasticity (STSP) may generate self-organized motor patterns. We simulated sphere-shaped autonomous robots, within the LPZRobots simulation package, containing three weights moving along orthogonal internal rods. The position of a weight is controlled by a single neuron receiving excitatory input from the sensor, measuring its actual position, and inhibitory inputs from the other two neurons. The inhibitory connections are transiently plastic, following physiologically inspired STSP-rules. We find that a wide palette of motion patterns are generated through the interaction of STSP, robot, and environment (closed-loop configuration), including various forward meandering and circular motions, together with chaotic trajectories. The observed locomotion is robust with respect to additional interactions with obstacles. In the chaotic phase the robot is seemingly engaged in actively exploring its environment. We believe that our results constitute a concept of proof that transient synaptic plasticity, as described by STSP, may potentially be important for the generation of motor commands and for the emergence of complex locomotion patterns, adapting seamlessly also to unexpected environmental feedback. We observe spontaneous and collision induced mode switchings, finding in addition, that locomotion may follow transiently limit cycles which are otherwise unstable. Regular locomotion corresponds to stable limit cycles in the sensorimotor loop, which may be characterized in turn by arbitrary angles of propagation. This degeneracy is, in our analysis, one of the drivings for the chaotic wandering observed for selected parameter settings, which is induced by the smooth diffusion of the angle of propagation.

q-bio.NC↗

arXiv2018

The sensorimotor loop as a dynamical system: How regular motion primitives may emerge from self-organized limit cycles

We investigate the sensorimotor loop of simple robots simulated within the LPZRobots environment from the point of view of dynamical systems theory. For a robot with a cylindrical shaped body and an actuator controlled by a single proprioceptual neuron we find various types of periodic motions in terms of stable limit cycles. These are self-organized in the sense, that the dynamics of the actuator kicks in only, for a certain range of parameters, when the barrel is already rolling, stopping otherwise. The stability of the resulting rolling motions terminates generally, as a function of the control parameters, at points where fold bifurcations of limit cycles occur. We find that several branches of motion types exist for the same parameters, in terms of the relative frequencies of the barrel and of the actuator, having each their respective basins of attractions in terms of initial conditions. For low drivings stable limit cycles describing periodic and drifting back-and-forth motions are found additionally. These modes allow to generate symmetry breaking explorative behavior purely by the timing of an otherwise neutral signal with respect to the cyclic back-and-forth motion of the robot.

q-bio.NC↗

arXiv2017

How to test for partially predictable chaos

For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation may split into an initial exponential decrease, characterized by the maximal Lyapunov exponent, and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. The time scales of both processes can be either of the same or of very different orders of magnitude. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and therefore remain partially predictable. Tests for distinguishing chaos from laminar flow widely use the time evolution of inter-orbital correlations as an indicator. Standard tests however yield mostly ambiguous results when it comes to distinguish partially predictable chaos and laminar flow, which are characterized respectively by attractors of fractally broadened braids and limit cycles. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories, showing that this test robustly discriminates chaos, including partially predictable chaos, from laminar flow. One can use furthermore the finite time cross-correlation of pairs of initially close trajectories to distinguish, for a complete classification, also between strong and partially predictable chaos. We are thus able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.

nlin.CD↗

arXiv2016

Time-scale effects on the gain-loss asymmetry in stock indices

The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over $2\%$, and it is the result of the non-Pearson type auto-correlations in the index. These non-Pearson type correlations can be viewed also as functionally dependent daily volatilities, extending for a finite time interval. A generalized time-window shuffling method is used to show the existence of such auto-correlations. Their characteristic time-scale proves to be smaller (less than $25$ trading days) than what was previously believed. It is also found that this characteristic time-scale has decreased with the appearance of program trading in the stock market transactions. Connections with the leverage effect are also established.

q-fin.ST↗

arXiv2015

A versatile class of prototype dynamical systems for complex bifurcation cascades of limit cycles

We introduce a versatile class of prototype dynamical systems for the study of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling bifurcations and transitions to chaos induced by sequences of limit cycle bifurcations. The prototype system consist of a $2d$-dimensional dynamical system with friction forces $f(V(\mathbf{x}))$ functionally dependent exclusively on the mechanical potential $V(\mathbf{x})$, which is typically characterized, here, by a finite number of local minima. We present examples for $d=1,2$ and simple polynomial friction forces $f(V)$, where the zeros of $f(V)$ regulate the relative importance of energy uptake and dissipation respectively, serving as bifurcation parameters. Starting from simple Hopf- and homoclinic bifurcations, complex sequences of limit cycle bifurcation are observed when energy uptake gains progressively in importance.

physics.comp-ph↗

arXiv2013

Chaos on the conveyor belt

The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by spring to an external static point, and due to the dragging effect of the belt the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can only be achieved by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic dynamics and phase transition-like behavior. Noise induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks, around five.

nlin.CD↗