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Sinha S. Emergent order in adaptively rewired networks. CHAOS (WOODBURY, N.Y.) 2024; 34:073151. [PMID: 39047160 DOI: 10.1063/5.0211829] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2024] [Accepted: 07/05/2024] [Indexed: 07/27/2024]
Abstract
We explore adaptive link change strategies that can lead a system to network configurations that yield ordered dynamical states. We propose two adaptive strategies based on feedback from the global synchronization error. In the first strategy, the connectivity matrix changes if the instantaneous synchronization error is larger than a prescribed threshold. In the second strategy, the probability of a link changing at any instant of time is proportional to the magnitude of the instantaneous synchronization error. We demonstrate that both these strategies are capable of guiding networks to chaos suppression within a prescribed tolerance, in two prototypical systems of coupled chaotic maps. So, the adaptation works effectively as an efficient search in the vast space of connectivities for a configuration that serves to yield a targeted pattern. The mean synchronization error shows the presence of a sharply defined transition to very low values after a critical coupling strength, in all cases. For the first strategy, the total time during which a network undergoes link adaptation also exhibits a distinct transition to a small value under increasing coupling strength. Analogously, for the second strategy, the mean fraction of links that change in the network over time, after transience, drops to nearly zero, after a critical coupling strength, implying that the network reaches a static link configuration that yields the desired dynamics. These ideas can then potentially help us to devise control methods for extended interactive systems, as well as suggest natural mechanisms capable of regularizing complex networks.
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Affiliation(s)
- Sudeshna Sinha
- Indian Institute of Science Education and Research Mohali, Knowledge City, SAS Nagar, Sector 81, Manauli PO 140 306, Punjab, India
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Ghomsi PG, Kakmeni FMM, Tchawoua C, Kofane TC. Synchronization of cells with activator-inhibitor pathways through adaptive environment-mediated coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052911. [PMID: 26651766 DOI: 10.1103/physreve.92.052911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2015] [Indexed: 06/05/2023]
Abstract
In this paper, we report the synchronized dynamics of cells with activator-inhibitor pathways via an adaptive environment-mediated coupling scheme with feedbacks and control mechanisms. The adaptive character of the extracellular medium is modeled via its damping parameter as a physiological response aiming at annihilating the cellular differentiation existing between the chaotic biochemical pathways of the cells, in order to preserve homeostasis. We perform an investigation on the existence and stability of the synchronization manifold of the coupled system under the proposed coupling pattern. Both mathematical and computational tools suggest the accessibility of conducive prerequisites (conditions) for the emergence of a robust synchronous regime. The relevance of a phase-synchronized dynamics is appraised and several numerical indicators advocate for the prevalence of this fascinating phenomenon among the interacting cells in the phase space.
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Affiliation(s)
- P Guemkam Ghomsi
- Complex systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63 Buea-CAMEROON and Laboratoire de Mécanique, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé-Cameroon
| | - F M Moukam Kakmeni
- Complex systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63 Buea-CAMEROON and International Centre of Insect Physiology and Ecology, P.O. Box 30772-00100, Nairobi, Kenya
| | - C Tchawoua
- Laboratoire de Mécanique, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé-Cameroon
| | - T C Kofane
- Laboratoire de Mécanique, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé-Cameroon
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Hackett-Jones EJ, Landman KA, Fellner K. Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041912. [PMID: 22680503 DOI: 10.1103/physreve.85.041912] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2011] [Indexed: 06/01/2023]
Abstract
Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach, and formally show a connection between the two. Interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive-repulsive potential are determined. For a swarming Morse potential, characteristic slow-fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches. The discrete approach is found to be remarkably robust to modifications in movement rules, related to the potential function. The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations.
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Affiliation(s)
- Emily J Hackett-Jones
- Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
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Levnajić Z, Tadić B. Stability and chaos in coupled two-dimensional maps on gene regulatory network of bacterium E. coli. CHAOS (WOODBURY, N.Y.) 2010; 20:033115. [PMID: 20887055 DOI: 10.1063/1.3474906] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
The collective dynamics of coupled two-dimensional chaotic maps on complex networks is known to exhibit a rich variety of emergent properties which crucially depend on the underlying network topology. We investigate the collective motion of Chirikov standard maps interacting with time delay through directed links of gene regulatory network of bacterium Escherichia coli. Departures from strongly chaotic behavior of the isolated maps are studied in relation to different coupling forms and strengths. At smaller coupling intensities the network induces stable and coherent emergent dynamics. The unstable behavior appearing with increase of coupling strength remains confined within a connected subnetwork. For the appropriate coupling, network exhibits statistically robust self-organized dynamics in a weakly chaotic regime.
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Affiliation(s)
- Zoran Levnajić
- Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Street 24/25, D-14476 Potsdam-Golm, Germany
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Miranda MA, Burguete J. Experimentally observed route to spatiotemporal chaos in an extended one-dimensional array of convective oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:046201. [PMID: 19518306 DOI: 10.1103/physreve.79.046201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2009] [Indexed: 05/27/2023]
Abstract
We report experimental evidence of the route to spatiotemporal chaos in a large one-dimensional array of hotspots in a thermoconvective system. As the driving force is increased, a stationary cellular pattern becomes unstable toward a mixed pattern of irregular clusters which consist of time-dependent localized patterns of variable spatiotemporal coherence. These irregular clusters coexist with the basic cellular pattern. The Fourier spectra corresponding to this synchronization transition reveal the weak coupling of a resonant triad. This pattern saturates with the formation of a unique domain of high spatiotemporal coherence. As we further increase the driving force, a supercritical bifurcation to a spatiotemporal beating regime takes place. The new pattern is characterized by the presence of two stationary clusters with a characteristic zig-zag geometry. The Fourier analysis reveals a stronger coupling than the previous mixed pattern and enables us to find out that this beating phenomenon is produced by the splitting of the fundamental spatiotemporal frequencies in a narrow band. Both secondary instabilities are phaselike synchronization transitions with global and absolute character. Far beyond this threshold, a new instability takes place when the system is not able to sustain the spatial frequency splitting, although the temporal beating remains inside these domains. These experimental results may support the understanding of other systems in nature undergoing similar clustering processes.
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Affiliation(s)
- M A Miranda
- Department of Physics and Applied Mathematics, Universidad de Navarra, Irunlarrea s/n, E-31080 Pamplona, Spain.
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Jabeen Z, Sinha S. Nonuniversal dependence of spatiotemporal regularity on randomness in coupling connections. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:066120. [PMID: 19256918 DOI: 10.1103/physreve.78.066120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2008] [Revised: 10/06/2008] [Indexed: 05/27/2023]
Abstract
We investigate the spatiotemporal dynamics of a network of coupled nonlinear oscillators, modeled by sine-circle maps, with varying degrees of randomness in coupling connections. We show that the change in the basin of attraction of the spatiotemporal fixed point due to varying fraction of random links, p , is crucially related to the nature of the local dynamics. Even the qualitative dependence of the spatiotemporal regularity on p changes drastically as the angular frequency of the oscillators changes, ranging from a monotonic increase or monotonic decrease to nonmonotonic variation. Thus it is evident here that the influence of random coupling connections on spatiotemporal order is highly nonuniversal and depends very strongly on the nodal dynamics.
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Mondal A, Sinha S, Kurths J. Rapidly switched random links enhance spatiotemporal regularity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:066209. [PMID: 19256927 DOI: 10.1103/physreve.78.066209] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2008] [Indexed: 05/27/2023]
Abstract
We investigate the spatiotemporal properties of a lattice of chaotic maps whose coupling connections are rewired to random sites with probability p . Keeping p constant, we change the random links at different frequencies in order to discern the effect (if any) of the time dependence of the links. We observe two different regimes in this network: (i) when the network is rewired slowly, namely, when the random connections are quite static, the dynamics of the network is spatiotemporally chaotic and (ii) when these random links are switched around fast, namely, the network is rewired frequently, one obtains a spatiotemporal fixed point over a large range of coupling strengths. We provide evidence of a sharp transition from a globally attracting spatiotemporal fixed point to spatiotemporal chaos as the rewiring frequency is decreased. Thus, in addition to geometrical properties such as the fraction of random links in the network, dynamical information on the time dependence of these links is crucial in determining the spatiotemporal properties of complex dynamical networks.
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Affiliation(s)
- Arghya Mondal
- Centre for Dynamics of Complex Systems, University of Potsdam, Potsdam D-14415, Germany
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Poria S, Shrimali MD, Sinha S. Enhancement of spatiotemporal regularity in an optimal window of random coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:035201. [PMID: 18851093 DOI: 10.1103/physreve.78.035201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2008] [Indexed: 05/26/2023]
Abstract
We investigate the spatiotemporal dynamics of a lattice of coupled chaotic maps whose coupling connections are dynamically rewired to random sites with probability p ; namely, at any instance of time, with probability p a regular link is switched to a random one. In a range of weak coupling, where spatiotemporal chaos exists for regular lattices (i.e., for p=0 ), we find that p>0 yields synchronized periodic orbits. Further, we observe that this regularity occurs over a window of p values, beyond which the basin of attraction of the synchronized cycle shrinks to zero. Thus we have evidence of an optimal range of randomness in coupling connections, where spatiotemporal regularity is efficiently obtained. This is in contrast to the commonly observed monotonic increase of synchronization with increasing p , as seen, for instance, in the strong-coupling regime of the very same system.
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Affiliation(s)
- Swarup Poria
- Department of Mathematics, Midnapore College, Midnapore 721 101, West Bengal, India.
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Rajesh S, Sinha S. Measuring collective behaviour of multicellular ensembles: role of space-time scales. J Biosci 2008; 33:289-301. [DOI: 10.1007/s12038-008-0046-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Hung YC, Huang YT, Ho MC, Hu CK. Paths to globally generalized synchronization in scale-free networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:016202. [PMID: 18351921 DOI: 10.1103/physreve.77.016202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2007] [Revised: 12/03/2007] [Indexed: 05/26/2023]
Abstract
We apply the auxiliary-system approach to study paths to globally generalized synchronization in scale-free networks of identical chaotic oscillators, including Hénon maps, logistic maps, and Lorentz oscillators. As the coupling strength epsilon between nodes of the network is increased, transitions from partially to globally generalized synchronization and intermittent behaviors near the synchronization thresholds, are found. The generalized synchronization starts from the hubs of the network and then spreads throughout the whole network with the increase of epsilon . Our result is useful for understanding the synchronization process in complex networks.
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Affiliation(s)
- Yao-Chen Hung
- Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan.
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Bragard J, Vidal G, Mancini H, Mendoza C, Boccaletti S. Chaos suppression through asymmetric coupling. CHAOS (WOODBURY, N.Y.) 2007; 17:043107. [PMID: 18163771 DOI: 10.1063/1.2797378] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We study pairs of identical coupled chaotic oscillators. In particular, we have used Roessler (in the funnel and no funnel regimes), Lorenz, and four-dimensional chaotic Lotka-Volterra models. In all four of these cases, a pair of identical oscillators is asymmetrically coupled. The main result of the numerical simulations is that in all cases, specific values of coupling strength and asymmetry exist that render the two oscillators periodic and synchronized. The values of the coupling strength for which this phenomenon occurs is well below the previously known value for complete synchronization. We have found that this behavior exists for all the chaotic oscillators that we have used in the analysis. We postulate that this behavior is presumably generic to all chaotic oscillators. In order to complete the study, we have tested the robustness of this phenomenon of chaos suppression versus the addition of some Gaussian noise. We found that chaos suppression is robust for the addition of finite noise level. Finally, we propose some extension to this research.
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Affiliation(s)
- J Bragard
- Department of Physics and Applied Math, Universidad de Navarra, Irunlarrea s/n, E-31080 Pamplona, Spain.
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