A zodiac of studies on complex systems
DOI:
https://doi.org/10.31349/SuplRevMexFis.1.4.32Keywords:
Nonlinear dynamics, complex systems, statistical physicsAbstract
We offer a brief description of a set of interrelated research lines on the physics of complex systems developed under a unifying methodology grown out from nonlinear dynamics of low dimensionality. The research lines were, and are, developed over a two-decade period (tacitly or not) under a simplifying assumption (and a posteriori corroboration) of a drastic reduction of degrees of freedom. The studies are conveniently grouped into twelve units, and these in turn into four groups, as in a zodiac. The studies in the first group, named Sensitivities, Glasses and Localizations, have in common a clear-cut original opening in the sense that, to our knowledge, the main tenet or result is not found elsewhere. Those in the second group, named Sums, Rankings and Fluctuations, have as a starting point previous stimulating studies or ideas that we followed up but then we converted into separate approaches. The subjects in the third group, named Networks, Measures and Games, involve preset work programs to be followed but ended up within unanticipated, perhaps deeper, grounds. The topics in the final fourth group, named Partitions, Diagonals and Windows, occurred, or are taking place, as specific technical goals that have become after belated realizations to be possible contributions towards the answer of fundamental quests. We discuss connections underlying different aspects of these investigations. Nonlinear dynamics
References
A. Robledo, Generalized statistical mechanics at the on- set of chaos, Entropy 15, 5178 (2013).
C. Velarde and A. Robledo, Manifestations of the onset of chaos in condensed matter and complex systems, European Physical Journal Special Topics 227, 645 (2018).
H. Schuster, Deterministic chaos. An Introduction, 2nd ed. (VCH Publishers, Weinheim, Germany, 1988).
C. Beck and F. Schlogl, Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge, UK, 1993).
R. Hilborn, Chaos and Nonlinear Dynamics, 2nd ed. (Oxford University Press, New York, NY, USA, 2000).
F. Baldovin and A. Robledo, Sensitivity to initial conditions at bifurcations in one-dimensional nonlinear maps: Rigorous nonextensive solutions, Europhysics Letters 60, 518 (2002).
F. Baldovin and A. Robledo, Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics, Physical Review E 66, 045104 (2002).
A. Robledo, Criticality in nonlinear one-dimensional maps: RG universal map and nonextensive entropy, Physica D: Nonlinear Phenomena 193, 153 (2004).
F. Baldovin and A. Robledo, Nonextensive Pesin identity: Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map, Physical Review E 69, 045202 (2004).
E. Mayoral and A. Robledo, Tsallis’ q index and Mori’s q phase transitions at the edge of chaos, Physical Review E 72, 026209 (2005).
H.Hernandez-Saldan ̃a and A.Robledo, Dynamics at the quasiperiodic onset of chaos, Tsallis q-statistics and
Mori’s q -phase thermodynamics, Physica A: Statistical Mechanics and its Applications 370, 286 (2006).
A. Robledo, Incidence of nonextensive thermodynamics in temporal scaling at Feigenbaum points, Physica A: Statistical Mechanics and its Applications 370, 449 (2006).
A. Robledo, Universal glassy dynamics at noise-perturbed onset of chaos: a route to ergodicity break-down, Physics Letters A 328, 467 (2004).
A. Robledo, Aging at the edge of chaos: Glassy dynamics and nonextensive statistics, Physica A: Statistical Mechanics and its Applications 342, 104 (2004).
F. Baldovin and A. Robledo, Glassy dynamics at the onset of chaos with additive noise, Fluctuation and Noise
Letters 5, L313 (2005).
F. Baldovin and A. Robledo, Parallels between the dy-
namics at the noise-perturbed onset of chaos in logistic maps and the dynamics of glass formation, Physical Re-view E 72, 066213 (2005).
M. Mart ́ınez-Mares and A. Robledo, Equivalence between the mobility edge of electronic transport on disorderless networks and the onset of chaos via intermittency in deterministic maps, Physical Review E 80, 045201 (2009).
Y. Jiang, M. Mart ́ınez-Mares, E. Castano, and A. Rob- ledo, Mo ̈bius transformations and electronic transport properties of large disorderless networks, Physical Review E 85, 057202 (2012).
M. Mart ́ınez-Mares, V. Dom ́ınguez-Rocha, and A. Rob- ledo, Typical length scales in conducting disorderless networks, European Physical Journal Special Topics 226, 417 (2017).
V. Dom ́ınguez-Rocha, R. M ́endez-Sa ́nchez, M. Mart ́ınez- Mares, and A. Robledo, Invariant density of intermittent nonlinear maps descriptive of coherent quantum transport through disorderless lattices, Physica D: Nonlinear Phenomena (2020, to be published).
M. A. Fuentes and A. Robledo, Renormalization group structure for sums of variables generated by incipiently chaotic maps, Journal of Statistical Mechanics: Theory and Experiment 2010, P01001 (2010).
M. A. Fuentes and A. Robledo, Stationary distributions of sums of marginally chaotic variables as renormalization group fixed points, in Journal of Physics: Confer- ence Series, Vol. 201 (IOP Publishing, 2010) p. 012002.
M. A. Fuentes and A. Robledo, Sums of variables at the onset of chaos, European Physical Journal B 87, 32
(2014).
A. D ́ıaz-Ruelas,M.A.Fuentes,and A.Robledo,Scaling
of distributions of sums of positions for chaotic dynamics at band-splitting points, Europhysics Letters 108, 20008 (2014).
A. Diaz-Ruelas and A. Robledo, Sums of variables at the onset of chaos, replenished, European Physical Journal Special Topics 225, 2763 (2016).
C. Altamirano and A. Robledo, Generalized thermody- namics underlying the laws of Zipf and Benford, in International Conference on Complex Sciences (Springer, 2009) pp. 2232–2237.
C. Altamirano and A. Robledo, Possible thermodynamic structure underlying the laws of Zipf and Benford, European Physical Journal B 81, 345 (2011).
A. Robledo, Laws of Zipf and Benford, intermittency, and critical fluctuations, Chinese Science Bulletin 56, 3643 (2011).
G. C. Yalcin, A. Robledo, and M. Gell-Mann, Incidence of q statistics in rank distributions, Proceedings of the National Academy of Sciences 111, 14082 (2014).
G. C. Yalcin, C. Velarde, and A. Robledo, Entropies for severely contracted configuration space, Heliyon 1, e00045 (2015).
C. Velarde and A. Robledo, Rank distributions: Frequency vs. magnitude, PLOS One 12, e0186015 (2017).
C. Velarde and A. Robledo, Dynamical analogues of rank distributions, PLOS One 14, 1 (2019).
A. Robledo, Unorthodox properties of critical clusters, Molecular Physics 103, 3025 (2005).
A. Robledo, q-statistical properties of large critical clusters, International Journal of Modern Physics B 21, 3947 (2007).
M. Riquelme-Galva ́n and A. Robledo, Dual characterization of critical fluctuations: Density functional theory & nonlinear dynamics close to a tangent bifurcation, European Physical Journal Special Topics 226, 433 (2017).
B. Luque, L. Lacasa, F. J. Ballesteros, and A. Robledo, Feigenbaum graphs: a complex network perspective of chaos, PLoS One 6 (2011).
B. Luque, L. Lacasa, F. J. Ballesteros, and A. Robledo, Analytical properties of horizontal visibility graphs in the Feigenbaum scenario, Chaos: An Interdisciplinary Jour- nal of Nonlinear Science 22, 013109 (2012).
B. Luque, L. Lacasa, and A. Robledo, Feigenbaum graphs at the onset of chaos, Physics Letters A 376, 3625 (2012).
B. Luque, F. J. Ballesteros, A. Nu ́n ̃ez, and A. Robledo, Quasiperiodic graphs: Structural design, scaling and entropic properties, Journal of Nonlinear Science 23, 335
(2013).
A. M. Nu ́n ̃ez, B. Luque, L. Lacasa, J. P. Go ́mez,
and A. Robledo, Horizontal visibility graphs generated by type-I intermittency, Physical Review E 87, 052801 (2013).
B. Luque, M. Cordero-Gracia, M. Go ́mez, and A. Robledo, Quasiperiodic graphs at the onset of chaos, Physical Review E 88, 062918 (2013).
B. Luque, F. J. Ballesteros, A. Robledo, and L. Lacasa, Entropy and renormalization in chaotic visibility graphs, in Mathematical Foundations and Applications of Graph Entropy, Vol. 6 (Wiley Online Library, 2017) pp. 1–39.
F. Baldovin, A. Diaz-Ruelas, and A. Robledo, Entropy of trajectories along period doubling and chaotic-band splitting cascades, Chaos: An Interdisciplinary Journal of Nonlinear Science (2020, in preparation).
D. Vilone, A. Robledo, and A. Sa ́nchez, Chaos and un- predictability in evolutionary dynamics in discrete time,
Physical Review Letters 107, 038101 (2011).
A. Diaz-Ruelas, H. J. Jensen, D. Piovani, and A. Rob- ledo, Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochas- tic dynamical system: The tangled nature model, Chaos: An Interdisciplinary Journal of Nonlinear Science 26,
(2016).
A. Diaz-Ruelas, H. J. Jensen, D. Piovani, and A. Rob-
ledo, Relating high dimensional stochastic complex sys- tems to low-dimensional intermittency, European Physical Journal Special Topics 226, 341–351 (2017).
A. Robledo and L. Moyano, Some aspects of the dynamics towards the supercycle attractors and their accumulation point, the Feigenbaum attractor, in AIP Conference Proceedings, Vol. 965 (American Institute of Physics, 2007) pp. 114–121.
A. Robledo and L. G. Moyano, q-deformed statistical- mechanical property in the dynamics of trajectories en route to the Feigenbaum attractor, Physical Review E 77, 036213 (2008).
L. Moyano, D. Silva, and A. Robledo, Labyrinthine pathways towards supercycle attractors in unimodal maps, Central European Journal of Physics 7, 591 (2009).
A. Robledo and L. Moyano, Dynamics towards the Feigenbaum attractor, Brazilian Journal of Physics 39, 364 (2009).
A. Robledo, q -deformed statistical-mechanical structure in the dynamics of the Feigenbaum attractor, in Journal of Physics: Conference Series, Vol. 246 (IOP Publishing, 2010) p. 012025.
A. Robledo, A dynamical model for hierarchy and mod- ular organization: The trajectories en route to the attractor at the transition to chaos, in Journal of Physics: Conference Series, Vol. 394 (IOP Publishing, 2012) p. 012007.
A. Diaz-Ruelas and A. Robledo, Emergent statistical- mechanical structure in the dynamics along the period-doubling route to chaos, Europhysics Letters 105, 40004 (2014).
A. Robledo, Self-organization and a constrained thermal system analogue of the onset of chaos, Europhysics Let- ters 123, 40003 (2018).
J. A. Yorke, C. Grebogi, E. Ott, and L. Tedeschini-Lalli, Scaling behavior of windows in dissipative dynamical systems, Physical Review Letters 54, 1095 (1985).
H. Capel and J. P. van der Weele, Window scaling in one- dimensional maps, Physics Letters A 136, 109 (1990).
V. Latora, A. Rapisarda, and A. Robledo, Revisiting disorder and Tsallis statistics, Science 300, 250 (2003).
A. Robledo, Unifying laws in multidisciplinary power-law phenomena: fixed-point universality and nonexten- sive entropy, in Nonextensive Entropy—Interdisciplinary Applications (Oxford University Press, 2004) pp. 63–77.
A. Robledo, Intermittency at critical transitions and aging dynamics at the onset of chaos, Pramana 64, 947 (2005).
A. Robledo, Critical attractors and q-statistics, Euro- physics News 36, 214 (2005).
A. Robledo, F. Baldovin, and E. Mayoral, Two stories outside Boltzmann-Gibbs statistics: Mori’s q -phase transitions and glassy dynamics at the onset of chaos, in Complexity, Metastability and Nonextensivity (World Scien- tific, 2005) pp. 43–54.
E. Mayoral and A. Robledo, A recent appreciation of the singular dynamics at the edge of chaos, in The Logistic Map and the Route to Chaos (Springer, 2006) pp. 339– 354.
A. Robledo, Crossover from critical to chaotic attractor dynamics in logistic and circle maps, Progress of Theoretical Physics Supplement 162, 10 (2006).
A. Robledo, Critical attractors and the physical realm
of q -statistics, in Chaos, Nonlinearity, Complexity (Springer, 2006) pp. 72–113.
A. Robledo, G ́enesis de una nueva f ́ısica estad ́ıstica, in Descubrimientos y Aportaciones Cient ́ıficas y Human ́ısticas Mexicanas en el Siglo Veinte (Academia Mexicana de Ciencias and Fondo de Cultura Econo ́mica, 2006).
C. Velarde and A. Robledo, Pascal (Yang Hui) triangles and power laws in the logistic map, in Journal of Physics: Conference Series, Vol. 604 (IOP Publishing, 2015) p. 012018.
M. Hill, Diversity and evenness: A unifying notation and its consequences, Ecology 54, 427 (1973).
T. Li, Nonlinear dynamics of traffic jams, Physica D: Nonlinear Phenomena 207, 41 (2005).
A. de Wijn, D. Miedema, B. Nienhuis, and P. Schall, Criticality in dynamic arrest: Correspondence between glasses and traffic, Physical Review Letters 109, 228001 (2012).
X.-J. W. P. Gaspard, Sporadicity: Between periodic and chaotic dynamical behaviors, Proceedings of the National Academy of Sciences 85, 4591 (1988).
S. A. Marvel, R. E. Mirollo, and S. H. Strogatz, Identical phase oscillators with global sinusoidal coupling evolve by Mo ̈bius group action, Chaos: An Interdisciplinary Journal of Nonlinear Science 19, 043104 (2009).
M. C. Mackey and M. Tyran-Kamin ́ska, Deterministic brownian motion: The effects of perturbing a dynamical system by a chaotic semi-dynamical system, Physics Reports 422, 167 (2006).
U. Tirnakli, C. Beck, and C. Tsallis, Central limit behavior of deterministic dynamical systems, Physical Review E 75, 040106(R) (2007).
U. Tirnakli, C. Tsallis, and C. Beck, Closer look at time averages of the logistic map at the edge of chaos, Physical Review E 79, 056209 (2009).
L. Pietronero, E. Tosatti, V. Tosatti, and A. Vespignani, The uneven distribution of numbers in nature., Physica A: Statistical Mechanics and its Applications 293, 297 (2001).
B. Hu and J. Rudnick, Exact solutions to the Feigenbaum renormalization-group equations for intermittency, Physical Review Letters 48, 1645 (1982).
N. G. Antoniou, Y. F. Contoyiannis, F. K. Diakonos, and C. G. Papadopoulos, Fractals at T = Tc due to instantonlike configurations, Physical Review Letters 81, 4289 (1998).
Y. Contoyiannis and F. Diakonos, Criticality and intermittency in the order parameter space, Physics Letters A 268, 286 (2000).
L. Lacasa, B. Luque, F. Ballesteros, J. Luque, and J. Nun ̃o, From time series to complex networks: the visibility graph, Proceedings of the National Academy of Sciences 105, 4972– (2008).
A. Robledo, Renormalization group, entropy optimization, and nonextensivity at criticality, Physical Review Letters 83, 2289 (1999).
N. van Kampen, Stochastic Processes in Physics and Chemistry, 3rd ed. (North Holland, Elsevier, BV, 2007).
P. Cvitanovic, Chaos: Classical and Quantum (Complexity Explorer, Santa Fe Institute, Santa Fe, USA, 2015).
P. Gaspard, Chaos,scattering and statistical mechanics
(Cambridge University Press, Cambridge, UK, 1998).
M. Nowak, Evolutionary Dynamics: Exploring the Equa- tions of Life (Belknap Press: An Imprint of Harvard University Press, Cambridge, MA, USA, 2006).
D. Piovani, J. Grujic, and H. Jensen, Linear stability the- ory as an early warning sign for transitions in high di- mensional complex systems, Journal of Physics A: Mathematical and Theoretical 49, 295102 (2016).
K. Christensen, S. di Collobiano, M. Hall, and H. Jensen, Tangled nature model: A model of evolutionary ecology,
Journal of Theoretical Biology 216, 2289 (2002).
G. Yule, A mathematical theory of evolution, Philosophical Transactions of the Royal Society B. 213, 21 (1925).
A.-L. Barab ́asi and R. Albert, Emergence of scaling in
random networks, Science 286, 509 (1999).
H. Jensen, Self-organized Criticality (Cambridge University Press, Cambridge, UK, 1998).
C. Ross, M. Odell, and S. Cremer, The shadow-curves of
the orbit diagram permeate the bifurcation diagram, too, International Journal of Bifurcation and Chaos 19, 3017 (2009).
E. Rosenberg and I. Zilber-Rosenberg, The Hologenome Concept: Human, Animal and Plant Microbiota (Springer International Publishing, Switzerland, 2013).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 Alberto Robledo Nieto, Luis Jovanny Camacho-Vidales
![Creative Commons License](http://i.creativecommons.org/l/by-nc-nd/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Suplemento de la Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.