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Sar GK, Ghosh D. Concept of swarming and synchrony in aquatic animal movements: Comment on "Control of movement of underwater swimmers: Animals, simulated animates and swimming robots" by Gordleeva et al. Phys Life Rev 2024; 49:1-3. [PMID: 38442457 DOI: 10.1016/j.plrev.2024.02.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2024] [Accepted: 02/27/2024] [Indexed: 03/07/2024]
Affiliation(s)
- Gourab Kumar Sar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
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2
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Ghosh S, Pal S, Sar GK, Ghosh D. Amplitude responses of swarmalators. Phys Rev E 2024; 109:054205. [PMID: 38907391 DOI: 10.1103/physreve.109.054205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2024] [Accepted: 04/17/2024] [Indexed: 06/24/2024]
Abstract
Swarmalators are entities that swarm through space and sync in time and are potentially considered to replicate the complex dynamics of many real-world systems. So far, the internal dynamics of swarmalators have been taken as a phase oscillator inspired by the Kuramoto model. Here we examine the internal dynamics utilizing an amplitude oscillator capable of exhibiting periodic and chaotic behaviors. To incorporate the dual interplay between spatial and internal dynamics, we propose a general model that keeps the properties of swarmalators intact. This adaptation calls for a detailed study, which we present in this paper. We establish our study with the Rössler oscillator by taking parameters from both chaotic and periodic regions. While the periodic oscillator mimics most of the patterns in the previous phase oscillator model, the chaotic oscillator brings some fascinating states.
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Affiliation(s)
- Samali Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Suvam Pal
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Gourab Kumar Sar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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3
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Sar GK, Ghosh D, O'Keeffe K. Solvable model of driven matter with pinning. Phys Rev E 2024; 109:044603. [PMID: 38755809 DOI: 10.1103/physreve.109.044603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 03/15/2024] [Indexed: 05/18/2024]
Abstract
We present a simple model of driven matter in a 1D medium with pinning impurities, applicable to magnetic domains walls, confined colloids, and other systems. We find rich dynamics, including hysteresis, reentrance, quasiperiodicity, and two distinct routes to chaos. In contrast to other minimal models of driven matter, the model is solvable: we derive the full phase diagram for small N, and for large N, we derive expressions for order parameters and several bifurcation curves. The model is also realistic. Its collective states match those seen in the experiments of magnetic domain walls.
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Affiliation(s)
- Gourab Kumar Sar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Kevin O'Keeffe
- Senseable City Lab, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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4
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Yadav A, J K, Chandrasekar VK, Zou W, Kurths J, Senthilkumar DV. Exotic swarming dynamics of high-dimensional swarmalators. Phys Rev E 2024; 109:044212. [PMID: 38755849 DOI: 10.1103/physreve.109.044212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Accepted: 03/28/2024] [Indexed: 05/18/2024]
Abstract
Swarmalators are oscillators that can swarm as well as sync via a dynamic balance between their spatial proximity and phase similarity. Swarmalator models employed so far in the literature comprise only one-dimensional phase variables to represent the intrinsic dynamics of the natural collectives. Nevertheless, the latter can indeed be represented more realistically by high-dimensional phase variables. For instance, the alignment of velocity vectors in a school of fish or a flock of birds can be more realistically set up in three-dimensional space, while the alignment of opinion formation in population dynamics could be multidimensional, in general. We present a generalized D-dimensional swarmalator model, which more accurately captures self-organizing behaviors of a plethora of real-world collectives by self-adaptation of high-dimensional spatial and phase variables. For a more sensible visualization and interpretation of the results, we restrict our simulations to three-dimensional spatial and phase variables. Our model provides a framework for modeling complicated processes such as flocking, schooling of fish, cell sorting during embryonic development, residential segregation, and opinion dynamics in social groups. We demonstrate its versatility by capturing the maneuvers of a school of fish, qualitatively and quantitatively, by a suitable extension of the original model to incorporate appropriate features besides a gallery of its intrinsic self-organizations for various interactions. We expect the proposed high-dimensional swarmalator model to be potentially useful in describing swarming systems and programmable and reconfigurable collectives in a wide range of disciplines, including the physics of active matter, developmental biology, sociology, and engineering.
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Affiliation(s)
- Akash Yadav
- School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Kerala 695551, India
| | - Krishnanand J
- School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Kerala 695551, India
| | - V K Chandrasekar
- Center for Nonlinear Science and Engineering, SASTRA Deemed University, Thanjavur, Tamil Nadu 613401, India
| | - Wei Zou
- School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany
- Institute of Physics, Humboldt University Berlin, D-12489 Berlin, Germany
- Research Institute of Intelligent Complex Systems, Fudan University, Shanghai 200433, China
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Kerala 695551, India
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5
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Lizárraga JUF, O'Keeffe KP, de Aguiar MAM. Order, chaos, and dimensionality transition in a system of swarmalators. Phys Rev E 2024; 109:044209. [PMID: 38755840 DOI: 10.1103/physreve.109.044209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Accepted: 03/20/2024] [Indexed: 05/18/2024]
Abstract
Similarly to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of these phenomena have been captured by collectives of hypothetical particles named swarmalators, each possessing a position and a phase whose dynamics are affected reciprocally and also by the space-phase states of their neighbors. In this work, we introduce a solvable model of swarmalators able to move in two-dimensional spaces. We show that several static and active collective states can emerge and derive necessary conditions for each to show up as the model parameters are varied. These conditions elucidate, in some cases, the displaying of multistability among states. Notably, in the active regime, the system exhibits hyperchaos, maintaining spatial correlation under certain conditions and breaking it under others on what we interpret as a dimensionality transition.
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Affiliation(s)
- Joao U F Lizárraga
- Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, São Paulo, Brazil
| | - Kevin P O'Keeffe
- Senseable City Lab, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Marcus A M de Aguiar
- Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, São Paulo, Brazil
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Kryuchkov NP, Nasyrov AD, Gursky KD, Yurchenko SO. Influence of anomalous agents on the dynamics of an active system. Phys Rev E 2024; 109:034601. [PMID: 38632726 DOI: 10.1103/physreve.109.034601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Accepted: 01/25/2024] [Indexed: 04/19/2024]
Abstract
Swarming behavior in systems of self-propelled particles, whether biological or artificial, has received increased attention in recent years. Here, we show that even a small number of particles with anomalous behavior can change dramatically collective dynamics of the swarming system and can impose unusual behavior and transitions between dynamic states. Our results pave the way to practical approaches and concepts of multiagent dynamics in groups of flocking animals: birds, insects, and fish, i.e., active and living soft matter.
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Affiliation(s)
- Nikita P Kryuchkov
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
| | - Artur D Nasyrov
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
| | - Konstantin D Gursky
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
| | - Stanislav O Yurchenko
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
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Pal S, Sar GK, Ghosh D, Pal A. Directional synchrony among self-propelled particles under spatial influence. CHAOS (WOODBURY, N.Y.) 2024; 34:021103. [PMID: 38363963 DOI: 10.1063/5.0188406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Accepted: 12/14/2023] [Indexed: 02/18/2024]
Abstract
Synchronization is one of the emerging collective phenomena in interacting particle systems. Its ubiquitous presence in nature, science, and technology has fascinated the scientific community over the decades. Moreover, a great deal of research has been, and is still being, devoted to understand various physical aspects of the subject. In particular, the study of interacting active particles has led to exotic phase transitions in such systems which have opened up a new research front-line. Motivated by this line of work, in this paper, we study the directional synchrony among self-propelled particles. These particles move inside a bounded region, and crucially their directions are also coupled with spatial degrees of freedom. We assume that the directional coupling between two particles is influenced by the relative spatial distance which changes over time. Furthermore, the nature of the influence is considered to be both short and long-ranged. We explore the phase transition scenario in both the cases and propose an approximation technique which enables us to analytically find the critical transition point. The results are further supported with numerical simulations. Our results have potential importance in the study of active systems like bird flocks, fish schools, and swarming robots where spatial influence plays a pertinent role.
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Affiliation(s)
- Suvam Pal
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Gourab Kumar Sar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Arnab Pal
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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Blum N, Li A, O'Keeffe K, Kogan O. Swarmalators with delayed interactions. Phys Rev E 2024; 109:014205. [PMID: 38366397 DOI: 10.1103/physreve.109.014205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2022] [Accepted: 09/15/2023] [Indexed: 02/18/2024]
Abstract
We investigate the effects of delayed interactions in a population of "swarmalators," generalizations of phase oscillators that both synchronize in time and swarm through space. We discover two steady collective states: a state in which swarmalators are essentially motionless in a disk arranged in a pseudocrystalline order, and a boiling state in which the swarmalators again form a disk, but now the swarmalators near the boundary perform boiling-like convective motions. These states are reminiscent of the beating clusters seen in photoactivated colloids and the living crystals of starfish embryos.
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Affiliation(s)
- Nicholas Blum
- California Polytechnic State University, San Luis Obispo, California 93407, USA
| | - Andre Li
- Department of Physics, California State University, East Bay, California 94542, USA
| | - Kevin O'Keeffe
- Senseable City Lab, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Oleg Kogan
- California Polytechnic State University, San Luis Obispo, California 93407, USA
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Hao B, Zhong M, O'Keeffe K. Attractive and repulsive interactions in the one-dimensional swarmalator model. Phys Rev E 2023; 108:064214. [PMID: 38243440 DOI: 10.1103/physreve.108.064214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Accepted: 11/30/2023] [Indexed: 01/21/2024]
Abstract
We study a population of swarmalators, mobile variants of phase oscillators, which run on a ring and have both attractive and repulsive interactions. This one-dimensional (1D) swarmalator model produces several of collective states: the standard sync and async states as well as a splaylike "polarized" state and several unsteady states such as active bands or swirling. The model's simplicity allows us to describe some of the states analytically. The model can be considered as a toy model for real-world swarmalators such as vinegar eels and sperm which swarm in quasi-1D geometries.
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Affiliation(s)
- Baoli Hao
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - Ming Zhong
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - Kevin O'Keeffe
- Senseable City Lab, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Sar GK, Ghosh D. Flocking and swarming in a multi-agent dynamical system. CHAOS (WOODBURY, N.Y.) 2023; 33:123126. [PMID: 38127290 DOI: 10.1063/5.0168050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Accepted: 11/20/2023] [Indexed: 12/23/2023]
Abstract
Over the past few decades, the research community has been interested in the study of multi-agent systems and their emerging collective dynamics. These systems are all around us in nature, such as bacterial colonies, fish schools, and bird flocks, as well as in technology, such as microswimmers and robotics, to name a few. Flocking and swarming are two key components of the collective behaviors of multi-agent systems. In flocking, the agents coordinate their direction of motion, but in swarming, they congregate in space to organize their spatial position. We propose a minimal mathematical model of a locally interacting multi-agent system where the agents simultaneously swarm in space and exhibit flocking behavior. Various cluster structures are found depending on the interaction range. When the coupling strength value exceeds a crucial threshold, flocking behavior is observed. We do in-depth simulations and report the findings by changing the other parameters and with the incorporation of noise.
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Affiliation(s)
- Gourab Kumar Sar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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Sar GK, O'Keeffe K, Ghosh D. Swarmalators on a ring with uncorrelated pinning. CHAOS (WOODBURY, N.Y.) 2023; 33:111103. [PMID: 37938924 DOI: 10.1063/5.0177024] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 10/10/2023] [Indexed: 11/10/2023]
Abstract
We present a case study of swarmalators (mobile oscillators) that move on a 1D ring and are subject to pinning. Previous work considered the special case where the pinning in space and the pinning in the phase dimension were correlated. Here, we study the general case where the space and phase pinning are uncorrelated, both being chosen uniformly at random. This induces several new effects, such as pinned async, mixed states, and a first-order phase transition. These phenomena may be found in real world swarmalators, such as systems of vinegar eels, Janus matchsticks, electrorotated Quincke rollers, or Japanese tree frogs.
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Affiliation(s)
- Gourab Kumar Sar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Kevin O'Keeffe
- Senseable City Lab, Massachusetts Institute of Technology, Cambridge Massachusetts 02139, USA
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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12
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Bomela W, Sebek M, Nagao R, Singhal B, Kiss IZ, Li JS. Finding influential nodes in networks using pinning control: Centrality measures confirmed with electrochemical oscillators. CHAOS (WOODBURY, N.Y.) 2023; 33:093128. [PMID: 37729101 PMCID: PMC10513758 DOI: 10.1063/5.0163899] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2023] [Accepted: 08/22/2023] [Indexed: 09/22/2023]
Abstract
The spatiotemporal organization of networks of dynamical units can break down resulting in diseases (e.g., in the brain) or large-scale malfunctions (e.g., power grid blackouts). Re-establishment of function then requires identification of the optimal intervention site from which the network behavior is most efficiently re-stabilized. Here, we consider one such scenario with a network of units with oscillatory dynamics, which can be suppressed by sufficiently strong coupling and stabilizing a single unit, i.e., pinning control. We analyze the stability of the network with hyperbolas in the control gain vs coupling strength state space and identify the most influential node (MIN) as the node that requires the weakest coupling to stabilize the network in the limit of very strong control gain. A computationally efficient method, based on the Moore-Penrose pseudoinverse of the network Laplacian matrix, was found to be efficient in identifying the MIN. In addition, we have found that in some networks, the MIN relocates when the control gain is changed, and thus, different nodes are the most influential ones for weakly and strongly coupled networks. A control theoretic measure is proposed to identify networks with unique or relocating MINs. We have identified real-world networks with relocating MINs, such as social and power grid networks. The results were confirmed in experiments with networks of chemical reactions, where oscillations in the networks were effectively suppressed through the pinning of a single reaction site determined by the computational method.
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Affiliation(s)
- Walter Bomela
- Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Michael Sebek
- Department of Physics and Center for Complex Network Research, Northeastern University, Boston, Massachusetts 02115, USA
| | - Raphael Nagao
- Institute of Chemistry, Department of Physical Chemistry, University of Campinas, Campinas, SP 13083-970, Brazil
| | - Bharat Singhal
- Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - István Z. Kiss
- Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA
| | - Jr-Shin Li
- Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA
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Ghosh S, Sar GK, Majhi S, Ghosh D. Antiphase synchronization in a population of swarmalators. Phys Rev E 2023; 108:034217. [PMID: 37849179 DOI: 10.1103/physreve.108.034217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 09/06/2023] [Indexed: 10/19/2023]
Abstract
Swarmalators are oscillatory systems endowed with a spatial component, whose spatial and phase dynamics affect each other. Such systems can demonstrate fascinating collective dynamics resembling many real-world processes. Through this work, we study a population of swarmalators where they are divided into different communities. The strengths of spatial attraction, repulsion, as well as phase interaction differ from one group to another. Also, they vary from intercommunity to intracommunity. We encounter, as a result of variation in the phase coupling strength, different routes to achieve the static synchronization state by choosing several parameter combinations. We observe that when the intercommunity phase coupling strength is sufficiently large, swarmalators settle in the static synchronization state. However, with a significant small phase coupling strength the state of antiphase synchronization as well as chimeralike coexistence of sync and async are realized. Apart from rigorous numerical results, we have been successful to provide semianalytical treatment for the existence and stability of global static sync and the antiphase sync states.
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Affiliation(s)
- Samali Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Gourab Kumar Sar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Soumen Majhi
- Department of Ecology and Evolution, University of Chicago, Chicago, Illinois 60637, USA
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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Lizárraga JUF, de Aguiar MAM. Synchronization of Sakaguchi swarmalators. Phys Rev E 2023; 108:024212. [PMID: 37723809 DOI: 10.1103/physreve.108.024212] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Accepted: 07/25/2023] [Indexed: 09/20/2023]
Abstract
Swarmalators are phase oscillators that cluster in space, like fireflies flashing in a swarm to attract mates. Interactions between particles, which tend to synchronize their phases and align their motion, decrease with the distance and phase difference between them, coupling the spatial and phase dynamics. In this work, we explore the effects of inducing phase frustration on a system of swarmalators that move on a one-dimensional ring. Our model is inspired by the well-known Kuramoto-Sakaguchi equations. We find, numerically and analytically, the ordered and disordered states that emerge in the system. The active states, not present in the model without frustration, resemble states found previously in numerical studies for the two-dimensional swarmalators system. One of these states, in particular, shows similarities to turbulence generated in a flattened media. We show that all ordered states can be generated for any values of the coupling constants by tuning the phase frustration parameters only. Moreover, many of these combinations display multistability.
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Affiliation(s)
- Joao U F Lizárraga
- Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, São Paulo, Brazil
| | - Marcus A M de Aguiar
- Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, São Paulo, Brazil
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