Model Of Self-propelled Particles Research Articles

Collective behaviors of animal groups may stem from visual lateralization—Tending to obtain information through one eye

Collective behaviors of animal groups may stem from visual lateralization—Tending to obtain information through one eye

Mechanistic modeling of alarm signaling in seed-harvester ants

<abstract><p>Ant colonies demonstrate a finely tuned alarm response to potential threats, offering a uniquely manageable empirical setting for exploring adaptive information diffusion within groups. To effectively address potential dangers, a social group must swiftly communicate the threat throughout the collective while conserving energy in the event that the threat is unfounded. Through a combination of modeling, simulation, and empirical observations of alarm spread and damping patterns, we identified the behavioral rules governing this adaptive response. Experimental trials involving alarmed ant workers (<italic>Pogonomyrmex californicus</italic>) released into a tranquil group of nestmates revealed a consistent pattern of rapid alarm propagation followed by a comparatively extended decay period <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>. The experiments in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup> showed that individual ants exhibiting alarm behavior increased their movement speed, with variations in response to alarm stimuli, particularly during the peak of the reaction. We used the data in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup> to investigate whether these observed characteristics alone could account for the swift mobility increase and gradual decay of alarm excitement. Our self-propelled particle model incorporated a switch-like mechanism for ants' response to alarm signals and individual variations in the intensity of speed increased after encountering these signals. This study aligned with the established hypothesis that individual ants possess cognitive abilities to process and disseminate information, contributing to collective cognition within the colony (see <sup>[<xref ref-type="bibr" rid="b2">2</xref>]</sup> and the references therein). The elements examined in this research support this hypothesis by reproducing statistical features of the empirical speed distribution across various parameter values.</p></abstract>

Applying collective motion models to study discordant individual behaviours within a school of fish.

Computational models of collective motion successfully reproduce the most common behaviours of a school of fish, using only a few elementary interactions between individuals. However, their ability to also reproduce individual behaviours that are discordant from those of the group has not yet been adequately investigated. In this paper, a self-propelled particle model using three interaction zones is considered in relation to the counter-rotation of an individual: a phenomenon observable in real schools of fish milling in a torus, when an individual moves in the same torus but in the opposite direction for a certain period of time. This study shows that the interactions of repulsion, orientation and attraction between individuals moving at constant speed in a three-dimensional space, with asynchronous updating, can generate temporary counter-rotations. The analysis of such events sheds light on the mechanisms that start the counter-rotation and those that end it. Although the contribution of the repulsion interaction is often significant to start and terminate the counter-rotation, it does not prove to be decisive. Indeed, it is observed that even when interactions between individuals are limited to attraction alone, temporary counter-rotations of individuals occur, provided the fish density along the circumference is not uniform. Some of these conclusions, deduced from the simulations performed, are visually consistent with what is observed in some underwater video recordings of milling schools of fish.

Control of Active Brownian Particles: An Exact Solution.

Control of stochastic systems is a challenging open problem in statistical physics, with a wealth of potential applications from biology to granulates. Unlike most cases investigated so far, we aim here at controlling a genuinely out-of-equilibrium system, the two dimensional active Brownian particles model in a harmonic potential, a paradigm for the study of self-propelled bacteria. We search for protocols for the driving parameters (stiffness of the potential and activity of the particles) bringing the system from an initial passivelike steady state to a final activelike one, within a chosen time interval. The exact analytical results found for this prototypical model of self-propelled particles brings control techniques to a wider class of out-of-equilibrium systems.

Using neuronal models to capture burst-and-glide motion and leadership in fish.

While mathematical models, in particular self-propelled particle models, capture many properties of large fish schools, they do not always capture the interactions of smaller shoals. Nor do these models tend to account for the use of intermittent locomotion, often referred to as burst-and-glide, by many species. In this paper, we propose a model of social burst-and-glide motion by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. We first show that our model can capture the motion of a single fish swimming down a channel. Extending to a two-fish model, where visual stimulus of a neighbour affects the internal burst or glide state of the fish, we observe a rich set of dynamics found in many species. These include: leader-follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and tit-for-tat turn taking. Moreover, unlike previous studies where a randomness is required for leadership switching to occur, we show that this can instead be the result of deterministic interactions. We give several empirically testable predictions for how bursting fish interact and discuss our results in light of recently established correlations between fish locomotion and brain activity.

Collective response to local perturbations: how to evade threats without losing coherence

Living groups move in complex environments and are constantly subject to external stimuli, predatory attacks and disturbances. An efficient response to such perturbations is vital to maintain the group’s coherence and cohesion. Perturbations are often local, i.e. they are initially perceived only by few individuals in the group, but can elicit a global response. This is the case of starling flocks, that can turn very quickly to evade predators. In this paper, we investigate the conditions under which a global change of direction can occur upon local perturbations. Using minimal models of self-propelled particles, we show that a collective directional response occurs on timescales that grow with the system size and it is, therefore, a finite-size effect. The larger the group is, the longer it will take to turn. We also show that global coherent turns can only take place if i) the mechanism for information propagation is efficient enough to transmit the local reaction undamped through the whole group; and if ii) motility is not too strong, to avoid that the perturbed individual leaves the group before the turn is complete. No compliance with such conditions results in the group’s fragmentation or in a non-efficient response.

Directional switches in network-organized swarming systems with delay.

Coordinated directional switches can emerge between members of moving biological groups. Previous studies have shown that the self-propelled particles model can well reproduce directional switching behaviors, but it neglects the impact of social interactions. Thus, we focus on the influence of social interactions on the ordered directional switching motion of swarming systems, in which homogeneous Erdös-Rényi networks, heterogeneous scale-free networks, networks with community structures, and real-world animal social networks have been considered. The theoretical estimation of mean switching time is obtained, and the results show that the interplay between social and delayed interactions plays an important role in regulating directional switching behavior. To be specific, for homogeneous Erdös-Rényi networks, the increase in mean degree may suppress the directional switching behaviors if the delay is sufficiently small. However, when the delay is large, the large mean degree may promote the directional switching behavior. For heterogeneous scale-free networks, the increase of degree heterogeneity can reduce the mean switching time if the delay is sufficiently small, while the increasing degree heterogeneity may suppress the ordered directional switches if the delay is large. For networks with community structures, higher communities can promote directional switches for small delays, while for large delays, it may inhibit directional switching behavior. For dolphin social networks, delay can promote the directional switching behavior. Our results bring to light the role of social and delayed interactions in the ordered directional switching motion.

Asymmetric Interactions Induce Bistability and Switching Behavior in Models of Collective Motion

Moving animal groups often spontaneously change their group structure and dynamics, but standard models used to explain collective motion in animal groups are typically unable to generate changes of this type. Recently, a model based on attraction, repulsion and asymmetric interactions designed for specific fish experiments was shown capable of producing such changes. However, the origin of the model’s ability to generate them, and the range of this capacity, remains unknown. Here we modify and extend this model to address these questions. We establish that its ability to generate groups exhibiting changes depends on the size of the blind zone parameter β. Specifically, we show that for small β swarms and mills are generated, for larger β polarized groups forms, and for a region of intermediate β values there is a bistability region where continuous switching between milling and polarized groups occurs. We also show that the location of the bistability region depends on group size and the relative strength of velocity alignment when this interaction is added to the model. These findings may contribute to advance the use of self-propelled particle models to explain a range of disruptive phenomena previously thought to be beyond the capabilities of such models.

Collective motion: Influence of local behavioural interactions among individuals

Fascinating patterns are displayed in nature due to the collective coherent motion of many living organisms. The origin of collective behaviours is diverse as the group members benefit in various ways: large resources of food, mating choices, nesting, and protection from predators, to name a few. It is still not well understood how complex behaviours emerge from a collective group that are otherwise not displayed at the level of solitary individuals. In recent years, along with field studies, numerous theoretical approaches have been developed to obtain insights into the mechanisms of aggregations and the collective decision-making processes. This brief review focuses on the self-propelled particle models, which have played a significant role in deciphering the underlying dynamics of collective motion in various organisms. Here, we discuss how local behavioural interactions and coordinations among the individual members give rise to complex collective behaviours. We consider the examples of collective motion in the schooling of fishes, flocking of birds, and swarming of prey, and address the emergence of a variety of patterns, a transition from disorder to ordered motion, and survival chances of prey group when under predator attacks.

Disordered Collective Motion in Dense Assemblies of Persistent Particles.

We explore the emergence of nonequilibrium collective motion in disordered nonthermal active matter when persistent motion and crowding effects compete, using simulations of a two-dimensional model of size polydisperse self-propelled particles. In stark contrast with monodisperse systems, we find that polydispersity stabilizes a homogeneous active liquid at arbitrary large persistence times, characterized by remarkable velocity correlations and irregular turbulent flows. For all persistence values, the active fluid undergoes a nonequilibrium glass transition at large density. This is accompanied by collective motion, whose nature evolves from near-equilibrium spatially heterogeneous dynamics at small persistence, to a qualitatively different intermittent dynamics when persistence is large. This latter regime involves a complex time evolution of the correlated displacement field.

Instability of Homogeneous State in Dynamical Models of Self-propelled Particles

Instability of Homogeneous State in Dynamical Models of Self-propelled Particles

Nonvanishing optimal noise in cellular automaton model of self-propelled particles

A minimal cellular automaton model is introduced to describe the collective motion of self-propelled particles on two-dimensional square lattice. The model features discretization of directional and positional spaces and single-particle occupation on one lattice site. Contrary to the Vicsek model and its variants, our model exhibits the nonvanishing optimal noise. When the particle density increases, the collective motion is promoted with optimal noise strength and reduced with noise strength out of optimal region. In addition, when the square lattice undergoes edge percolation process, no abrupt change of alignment behaviors is observed at the critical point of percolation.

Attraction vs. Alignment as Drivers of Collective Motion

Moving animal groups exhibit a range of fascinating behaviors. The standard explanation for how these groups form and function is that the individual animals interact via attraction, repulsion, and alignment, where alignment is proposed to drive the collective motion. However, it has been shown both experimentally and theoretically that alignment interactions are not required to induce group level alignment. In particular, via the use of self-propelled particle models it has been established that several other mechanisms induce group level alignment (aka polarization) in combination with attraction alone. However, no systematic comparison of these mechanisms among themselves, or with explicit alignment, has been presented and it remains unclear how, or even if, they can be distinguished at the collective level. Here, we introduce two previously unreported mechanisms, burst-and-glide and burst-and-stop, and show via simulation that they also induce polarization in combination with attraction alone. Then, we compare the polarization inducing characteristics of six mechanisms; asymmetric interactions, asynchrony, anticipation, burst-and-glide, burst-and stop, and explicit alignment. We show that the mechanisms induce polarization in different parts of the attraction parameter space, that the route to polarization from uniformly random initial conditions, as well as repolarization following strong perturbations, is markedly different among the mechanisms. In particular, we find that alignment based and non-alignment based mechanisms can be distinguished via their polarization and repolarization processes. These findings further challenge the current alignment based theory of collective motion and may contribute to a more versatile theory of collective motion across scales.

Dominating lengthscales of zebrafish collective behaviour.

Collective behaviour in living systems is observed across many scales, from bacteria to insects, to fish shoals. Zebrafish have emerged as a model system amenable to laboratory study. Here we report a three-dimensional study of the collective dynamics of fifty zebrafish. We observed the emergence of collective behaviour changing between ordered to randomised, upon adaptation to new environmental conditions. We quantify the spatial and temporal correlation functions of the fish and identify two length scales, the persistence length and the nearest neighbour distance, that capture the essence of the behavioural changes. The ratio of the two length scales correlates robustly with the polarisation of collective motion that we explain with a reductionist model of self-propelled particles with alignment interactions.

Phases and homogeneous ordered states in alignment-based self-propelled particle models.

We study a set of models of self-propelled particles that achieve collective motion through similar alignment-based dynamics, considering versions with and without repulsive interactions that do not affect the heading directions. We explore their phase space within a broad range of values of two nondimensional parameters (coupling strength and Peclet number), characterizing their polarization and degree of clustering. The resulting phase diagrams display equivalent, similarly distributed regions for all models with repulsion. The diagrams without repulsion exhibit differences, in particular for high coupling strengths. We compare the boundaries and representative states of all regions, identifying various regimes that had not been previously characterized. We analyze in detail three types of homogeneous polarized states, comparing them to existing theoretical and numerical results by computing their velocity and density correlations, giant number fluctuations, and local order-density coupling. We find that they all deviate in one way or another from the theoretical predictions, attributing these differences either to the remaining inhomogeneities or to finite-size effects. We discuss our results in terms of the generic or specific features of each model, their thermodynamic limit, and the high mixing and low mixing regimes. Our study provides a broad, overarching perspective on the multiple phases and states found in alignment-based self-propelled particle models.

Efficient flocking: metric versus topological interactions.

Flocking is a fascinating phenomenon observed across a wide range of living organisms. We investigate, based on a simple self-propelled particle model, how the emergence of ordered motion in a collectively moving group is influenced by the local rules of interactions among the individuals, namely, metric versus topological interactions as debated in the current literature. In the case of the metric ruling, the individuals interact with the neighbours within a certain metric distance; by contrast, in the topological ruling, interaction is confined within a number of fixed nearest neighbours. Here, we explore how the range of interaction versus the number of fixed interacting neighbours affects the dynamics of flocking in an unbounded space, as observed in natural scenarios. Our study reveals the existence of a certain threshold value of the interaction radius in the case of metric ruling and a threshold number of interacting neighbours for the topological ruling to reach an ordered state. Interestingly, our analysis shows that topological interaction is more effective in bringing the order in the group, as observed in field studies. We further compare how the nature of the interactions affects the dynamics for various sizes and speeds of the flock.

Diffusion of active particles with angular velocity reversal.

Biological and synthetic microswimmers display a wide range of swimming trajectories depending on driving forces and torques. In this paper we consider a simple overdamped model of self-propelled particles with a constant self-propulsion speed but an angular velocity that varies in time. Specifically, we consider the case of both deterministic and stochastic angular velocity reversals, mimicking several synthetic active matter systems, such as propelled droplets. The orientational correlation function and effective diffusivity is studied using Langevin dynamics simulations and perturbative methods.

Can playing Spirograph lead to an ordered structure in self-propelled particles?

Understanding the local dynamics of microorganisms infecting a cell could help us develop efficient strategies to counter their aggregation. In the present study we have introduced a simple model of self-propelled particles (SPPs) with constant linear velocity, both in 2 and 3 dimensions, which captures the essential features of a microorganism's aggregation as well the dynamics around an attractive point (AP). The static behavior shows the presence of an icosahedral structure for a finite number of SPPs, and a hexagonal closed packed structure for an infinite number of SPPs, which was confirmed using Steinhardt bond order parameters for a 3-dimensional model. For a single SPP the dynamic behaviour involves the formation of orbits around the AP, which can be categorised into three dynamical regions based on the strength of coupling between the AP and SPP. For weak coupling we observe a rosette-like trajectory reminiscent of the pattern formed by the Spirograph toy. For intermediate coupling, circular trajectories were observed, and for very strong coupling the SPP was static and was always aligned with the AP. The radial distance from the AP to SPP was determined by the angular velocities of the SPP for the rosette-like region whereas for the circular and static regions, it was determined by the coupling constant. Even for a finite number of SPPs we observed the same behavior as long as the SPPs could rotate around the AP without colliding with each other.

Behavioral response of insecticide-resistant mosquitoes against spatial repellent: A modified self-propelled particle model simulation.

Rapidly increasing pyrethroid insecticide resistance and changes in vector biting and resting behavior pose serious challenges in malaria control. Mosquito repellents, especially spatial repellents, have received much attention from industry. We attempted to simulate interactions between mosquitoes and repellents using a machine learning method, the Self-Propelled Particle (SPP) model, which we modified to include attractiveness/repellency effects. We simulated a random walk scenario and scenarios with insecticide susceptible/resistant mosquitoes against repellent alone and against repellent plus attractant (to mimic a human host). Simulation results indicated that without attractant/repellent, mosquitoes would fly anywhere in the cage at random. With attractant, all mosquitoes were attracted to the source of the odor by the end. With repellent, all insecticide-susceptible mosquitoes eventually moved to the corner of the cage farthest from the repellent release point, whereas, a high proportion of highly resistant mosquitoes might reach the attractant release point (the human) earlier in the simulation. At fixed concentration, a high proportion of mosquitoes could be able to reach the host when the relative repellency efficacy (compare to attractant efficacy) was <1, whereas, no mosquitoes reached the host when the relative repellency efficacy was > 1. This result implies that repellent may not be sufficient against highly physiologically insecticide resistant mosquitoes, since very high concentrations of repellent are neither practically feasible nor cost-effective.

Lévy Walk in Swarm Models Based on Bayesian and Inverse Bayesian Inference.

While swarming behavior is regarded as a critical phenomenon in phase transition and frequently shows the properties of a critical state such as Lévy walk, a general mechanism to explain the critical property in swarming behavior has not yet been found. Here, we address this problem with a simple swarm model, the Self-Propelled Particle (SPP) model, and propose a way to explain this critical behavior by introducing agents making decisions via the data-hypothesis interaction in Bayesian inference, namely, Bayesian and inverse Bayesian inference (BIB). We compare three SPP models, namely, the simple SPP, the SPP with Bayesian-only inference (BO) and the SPP with BIB models. We show that only the BIB model entails coexisting tornado, splash and translation behaviors, and the Lévy walk pattern.