Cristián Huepe

Inferring the structure and dynamics of interactions in schooling fish

Determining individual-level interactions that govern highly coordinated motion in animal groups or cellular aggregates has been a long-standing challenge, central to understanding the mechanisms and evolution of collective behavior. Numerous models have been proposed, many of which display realistic-looking dynamics, but nonetheless rely on untested assumptions about how individuals integrate information to guide movement. Here we infer behavioral rules directly from experimental data. We begin by analyzing trajectories of golden shiners (Notemigonus crysoleucas) swimming in two-fish and three-fish shoals to map the mean effective forces as a function of fish positions and velocities. Speeding and turning responses are dynamically modulated and clearly delineated. Speed regulation is a dominant component of how fish interact, and changes in speed are transmitted to those both behind and ahead. Alignment emerges from attraction and repulsion, and fish tend to copy directional changes made by those ahead. We find no evidence for explicit matching of body orientation. By comparing data from two-fish and three-fish shoals, we challenge the standard assumption, ubiquitous in physics-inspired models of collective behavior, that individual motion results from averaging responses to each neighbor considered separately; three-body interactions make a substantial contribution to fish dynamics. However, pairwise interactions qualitatively capture the correct spatial interaction structure in small groups, and this structure persists in larger groups of 10 and 30 fish. The interactions revealed here may help account for the rapid changes in speed and direction that enable real animal groups to stay cohesive and amplify important social information.

Phase transitions in systems of self-propelled agents and related network models

An important characteristic of flocks of birds, schools of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system.

Collective States, Multistability and Transitional Behavior in Schooling Fish

The spontaneous emergence of pattern formation is ubiquitous in nature, often arising as a collective phenomenon from interactions among a large number of individual constituents or sub-systems. Understanding, and controlling, collective behavior is dependent on determining the low-level dynamical principles from which spatial and temporal patterns emerge; a key question is whether different group-level patterns result from all components of a system responding to the same external factor, individual components changing behavior but in a distributed self-organized way, or whether multiple collective states co-exist for the same individual behaviors. Using schooling fish (golden shiners, in groups of 30 to 300 fish) as a model system, we demonstrate that collective motion can be effectively mapped onto a set of order parameters describing the macroscopic group structure, revealing the existence of at least three dynamically-stable collective states; swarm, milling and polarized groups. Swarms are characterized by slow individual motion and a relatively dense, disordered structure. Increasing swim speed is associated with a transition to one of two locally-ordered states, milling or highly-mobile polarized groups. The stability of the discrete collective behaviors exhibited by a group depends on the number of group members. Transitions between states are influenced by both external (boundary-driven) and internal (changing motion of group members) factors. Whereas transitions between locally-disordered and locally-ordered group states are speed dependent, analysis of local and global properties of groups suggests that, congruent with theory, milling and polarized states co-exist in a bistable regime with transitions largely driven by perturbations. Our study allows us to relate theoretical and empirical understanding of animal group behavior and emphasizes dynamic changes in the structure of such groups.

Phase transitions in Self-Driven many-particle systems and related non-equilibrium models: A network approach

We investigate the conditions that produce a phase transition from an ordered to a disordered state in a family of models of two-dimensional elements with a ferromagnetic-like interaction. This family is defined to contain under the same framework, among others, the XY-model and the Self-Driven Particles Model introduced by Vicsek et al. Each model is distinguished only by the rules that determine the set of elements with which each element interacts. We propose a new member of the family: the vectorial network model, in which a given fraction of the elements interact through direct random connections. This model is analogous to an XY-system on a network, and as such can be of interest for a wide range of problems. It captures the main aspects of the interaction dynamics that produce the phase transition in other models of the family. The network approach allows us to show analytically the existence of a phase transition in this vectorial network model, and to compute its relevant parameters for the case in which all elements are randomly connected. Finally we study numerically the conditions required for a phase transition to exist for different members of the family. Our results show that a qualitatively equivalent phase transition appears whenever even a small amount of long-range interactions are present (or built over time), regardless of other equilibrium or non-equilibrium properties of the system.

Adaptive-network models of swarm dynamics

We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model using a low-dimensional system of equations permitting analytical investigation. We find that the model reproduces several characteristic features of swarms, including spontaneous symmetry breaking, noise- and density-driven order-disorder transitions that can be of first or second order, and intermittency. Reproducing these experimental observations using a non-spatial model suggests that spatial geometry may have less of an impact on collective motion than previously thought.

Self-organized flocking with a mobile robot swarm: a novel motion control method

In flocking, a swarm of robots moves cohesively in a common direction. Traditionally, flocking is realized using two main control rules: proximal control, which controls the cohesion of the swarm using local range-and bearing information about neighboring robots; and alignment control, which allows the robots to align in a common direction and uses more elaborate sensing mechanisms to obtain the orientation of neighboring robots. So far, limited attention has been given to motion control, used to translate the output of these two control rules into robot motion. In this paper, we propose a novel motion control method: magnitude-dependent motion control (MDMC). Through simulations and real robot experiments, we show that, with MDMC, flocking in a random direction is possible without the need for alignment control and for robots having a preferred direction of travel. MDMC has the advantage to be implementable on very simple robots that lack the capability to detect the orientation of their neighbors. In addition, we introduce a small proportion of robots informed about a desired direction of travel. We compare MDMC with a motion control method used in previous robotics literature, which we call magnitude-independent motion control (MIMC), and we show that the swarms can travel longer distances in the desired direction when using MDMC instead of MIMC. Finally, we systematically study flocking under various conditions: with or without alignment control, with or without informed robots, with MDMC or with MIMC.

Collective dynamics of self-propelled particles with variable speed

Understanding the organization of collective motion in biological systems is an ongoing challenge. In this paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish, we introduce a power-law dependency of the speed of each particle on the degree of polarization order in its neighborhood. We derive analytically a coarse-grained continuous approximation for this model and find that, while the specific variable speed rule used does not change the details of the ordering transition leading to collective motion, it induces an inverse power-law correlation between the speed or the local polarization order and the local density. Using numerical simulations, we verify the range of validity of this continuous description and explore regimes beyond it. We discover, in disordered states close to the transition, a phase-segregated regime where most particles cluster into almost static groups surrounded by isolated high-speed particles. We argue that the mechanism responsible for this regime could be present in a wide range of collective motion dynamics.

Dynamical phase transition in a neural network model with noise: an exact solution

The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same value. It is shown that, under very general conditions, there exists a critical value ηc of the noise, below which the network remains organized and above which it behaves randomly. The existence and nature of the phase transition are computed analytically, showing that the critical exponent is 1/2. The dependence of ηc on the parameters of the network is obtained. These results are then compared with two numerical realizations of the network.

Scaling laws for vortical nucleation solutions in a model of superflow

The bifurcation diagram corresponding to stationary solutions of the nonlinear Schrodinger equation describing a superflow around a disc is numerically computed using continuation techniques. When the Mach number is varied, it is found that the stable and unstable (nucleation) branches are connected through a primary saddle-node and a secondary pitchfork bifurcation. Computations are carried out for values of the ratio =d of the coherence length to the diameter of the disc in the range 1/5‐1/80. It is found that the critical velocity converges for =d ! 0 to an Eulerian value, with a scaling compatible with previous investigations. The energy barrier for nucleation solutions is found to scale as 2 . Dynamical solutions are studied and the frequency of supercritical vortex shedding is found to scale as the square root of the bifurcation parameter.

Stability and decay rates of nonisotropic attractive Bose-Einstein condensates

Nonisotropic attractive Bose-Einstein condensates are investigated numerically with Newton and inverse Arnoldi methods. The stationary solutions of the Gross-Pitaevskii equation and their linear stability are computed. Bifurcation diagrams are calculated and used to find the condensate decay rates corresponding to macroscopic quantum tunneling, two-three-body inelastic collisions, and thermally induced collapse. Isotropic and nonisotropic condensates are compared. The effect of anisotropy on the bifurcation diagram and the decay rates is discussed. Spontaneous isotropization of the condensates is found to occur. The influence of isotropization on the decay rates is characterized near the critical point.