Confined System Analysis of a Predator-Prey Minimalistic Model

Collective anti-predator escape manoeuvres through optimal attack and avoidance strategies

The collective dynamics of self-organised systems emerge from the decision rules agents use to respond to each other and to external forces. This is evident in groups of animals under attack from predators, where understanding collective escape patterns requires evaluating the risks and rewards associated with particular social rules, prey escape behaviour, and predator attack strategies. Here, we find that the emergence of the 'fountain effect', a common collective pattern observed when animal groups evade predators, is the outcome of rules designed to maximise individual survival chances given predator hunting decisions. Using drone-based empirical observations of schooling sardine prey (Sardinops sagax caerulea) attacked by striped marlin (Kajikia audax), we first find the majority of attacks produce fountain effects, with the dynamics of these escapes dependent on the predator's attack direction. Then, using a spatially-explicit agent-based model of predator-prey dynamics, we show that fountain manoeuvres can emerge from combining an optimal individual prey escape angle with social interactions. The escape rule appears to prioritise maximising the distance to the predator and creates conflict in the effectiveness of predators' attacks and the prey's avoidance, explaining the empirically observed predators' attack strategies and the fountain evasions produced by prey. Overall, we identify the proximate and ultimate explanations for fountain effects and more generally highlight that the collective patterns of self-organised predatory-prey systems can be understood by considering both social escape rules and attack strategies.

Emergence of collective behaviours from local Voronoi topological perception

This article addresses how diverse collective behaviours arise from simple and realistic decisions made entirely at the level of each agent's personal space in the sense of the Voronoi diagram. We present a discrete-time model in two dimensions in which individual agents are aware of their local Voronoi environment and may seek static target locations. In particular, agents only communicate directly with their Voronoi neighbours and make decisions based on the geometry of their own Voronoi cells. With two effective control parameters, it is shown numerically to capture a wide range of collective behaviours in different scenarios. Further, we show that the Voronoi topology facilitates the computation of several novel observables for quantifying discrete collective behaviours. These observables are applicable to all agent-based models and to empirical data.

Inertial effect on evasion and pursuit dynamics of prey swarms: the emergence of a favourable mass ratio for the predator-prey arms race

We show, based on a theoretical model, how inertia plays a pivotal role in the survival dynamics of a prey swarm while chased by a predator. With the varying mass of the prey and predator, diverse escape patterns emerge, such as circling, chasing, maneuvering, dividing into subgroups, and merging into a unitary group, similar to the escape trajectories observed in nature. Moreover, we find a transition from non-survival to survival of the prey swarm with increasing predator mass. The transition regime is also sensitive to the variation in prey mass. Further, the analysis of the prey group survival as a function of predator-to-prey mass ratio unveils the existence of three distinct regimes: (i) frequent chase and capture leading to the non-survival of the prey swarm, (ii) an intermediate regime where competition between pursuit and capture occurs, resembling an arms race, and (iii) the survival regime without the capture of prey. Interestingly, our study demonstrates the existence of a favourable predator-prey mass ratio for coexistence of both prey and predator in an ecosystem, which agrees well with the field studies.

Fish-inspired robotic algorithm: mimicking behaviour and communication of schooling fish

This study aims to present a novel flocking algorithm for robotic fish that will aid the study of fish in their natural environment. The algorithm, fish-inspired robotic algorithm (FIRA), amalgamates the standard flocking behaviors of attraction, alignment, and repulsion, together with predator avoidance, foraging, general obstacle avoidance, and wandering. The novelty of the FIRA algorithm is the combination of predictive elements to counteract processing delays from sensors and the addition of memory. Furthermore, FIRA is specifically designed to work with an indirect communication method that leads to superior performance in collision avoidance, exploration, foraging, and the emergence of realistic behaviors. By leveraging a high-latency, non-guaranteed communication methodology inspired by stigmergy methods inherent in nature, FIRA successfully addresses some of the obstacles associated with underwater communication. This breakthrough enables the realization of inexpensive, multi-agent swarms while concurrently harnessing the advantages of tetherless communication. FIRA provides a computational light control algorithm for further research with low-cost, low-computing agents. Eventually, FIRA will be used to assimilate robots into a school of biological fish, to study or influence the school. This study endeavors to demonstrate the effectiveness of FIRA by simulating it using a digital twin of a bio-inspired robotic fish. The simulation incorporates the robot's motion and sensors in a realistic, real-time environment with the algorithm used to direct the movements of individual agents. The performance of FIRA was tested against other collective flocking algorithms to determine its effectiveness. From the experiments, it was determined that FIRA outperformed the other algorithms in both collision avoidance and exploration. These experiments establish FIRA as a viable flocking algorithm to mimic fish behavior in robotics.

Enhancing search efficiency through diffusive echo

Despite having been studied for decades, first passage processes remain an active area of research. In this contribution we examine a particle diffusing in an annulus with an inner absorbing boundary and an outer reflective boundary. We obtain analytic expressions for the joint distribution of the hitting time and the hitting angle in two and three dimensions. For certain configurations we observe a ``diffusive echo", i.e. two well-defined maxima in the first passage time distribution to a targeted position on the absorbing boundary. This effect, which results from the interplay between the starting location and the environmental constraints, may help to significantly increase the efficiency of the random search by generating a high, sustained flux to the targeted position over a short period. Finally, we examine the corresponding one-dimensional system for which there is no well-defined echo. In a confined system, the flux integrated over all target positions always displays a shoulder. This does not, however, guarantee the presence of an echo in the joint distribution.

Spatiotemporal dynamics of a self-propelled system with opposing alignment and repulsive forces

Effect of concurrent alignment and repulsion is studied in the purview of a confined active matter system using a modified force-based Vicsek model. On alteration of the alignment and the repulsive force parameters, a low alignment random phase, a midrange alignment milling phase, and a high alignment oscillatory phase are identified. Based on the particle aggregations, the milling phase is further classified into three subphases, two of which are spatial patterns: one consisting of compact ring-shaped mills and the other incorporating both rings and clusters. A correlation function based on the inner product of spatial velocity fluctuations of the particles shows a high correlation length for the ringed milling and the rings-clusters hybrid milling state. On analyzing temporal velocity fluctuations of particles through chaos detection techniques, low alignment and high alignment states are indicative of chaos, while the middle order alignment is symbolic of periodicity. The extent of synchronization of the particles' motion is analyzed through a Hilbert transform-based mean frequency approach, leading to the detection of a weak chimera state in the case of the spatial structures. The ringed milling state shows a unique category of weak chimera consisting of multiple oscillator groups showcasing different synchronization frequencies coexisting with desynchronized oscillators.

Effect of particle fraction on phase transitions in an active-passive particles system

We study phase transition in a binary system of monodisperse active and passive particles. The particles are initially randomly positioned inside a fixed boundary square enclosure. The active particles can move with their self-propulsion force. Whereas, the passive particles do not have any self-propulsion force, and they move by the spatial interactions with other particles. An alignment force in our discrete element model causes the emergence of collective milling motion. Without this alignment interaction, the particle system remains in a disordered phase. Whereas, the ordered milling phase is attained after achieving a minimum coordination among neighboring particles. The phase transition from disordered to ordered depends upon the relative effect of self-propulsion and the alignment, initial states of the particles, noise level, and the fraction of the active particles present in the system. The phase transition we observed is of first-order nature.