Invariable distribution of co-evolutionary complex adaptive systems with agent's behavior and local topological configuration

Hebing Zhang; Xiaojing Zheng; Hebing Zhang; Xiaojing Zheng

doi:10.3934/mbe.2024143

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 2: 3229-3261. doi: 10.3934/mbe.2024143

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Invariable distribution of co-evolutionary complex adaptive systems with agent's behavior and local topological configuration

Hebing Zhang ¹,
Xiaojing Zheng ^{2
,
,}

1.
School of Intelligent Manufacture, Taizhou University, Jiaojiang 318000, Zhejiang, China
2.
Weifang University of Science and Technology, Shouguang 262700, Shandong, China

Received: 06 December 2023 Revised: 24 January 2024 Accepted: 25 January 2024 Published: 01 February 2024

In this study, we developed a dynamical Multi-Local-Worlds (MLW) complex adaptive system with co-evolution of agent's behavior and local topological configuration to predict whether agents' behavior would converge to a certain invariable distribution and derive the conditions that should be satisfied by the invariable distribution of the optimal strategies in a dynamical system structure. To this end, a Markov process controlled by agent's behavior and local graphic topology configuration was constructed to describe the dynamic case's interaction property. After analysis, the invariable distribution of the system was obtained using the stochastic process method. Then, three kinds of agent's behavior (smart, normal, and irrational) coupled with corresponding behaviors, were introduced as an example to prove that their strategies converge to a certain invariable distribution. The results showed that an agent selected his/her behavior according to the evolution of random complex networks driven by preferential attachment and a volatility mechanism with its payment, which made the complex adaptive system evolve. We conclude that the corresponding invariable distribution was determined by agent's behavior, the system's topology configuration, the agent's behavior noise, and the system population. The invariable distribution with agent's behavior noise tending to zero differed from that with the population tending to infinity. The universal conclusion, corresponding to the properties of both dynamical MLW complex adaptive system and cooperative/non-cooperative game that are much closer to the common property of actual economic and management events that have not been analyzed before, is instrumental in substantiating managers' decision-making in the development of traffic systems, urban models, industrial clusters, technology innovation centers, and other applications.
- Complex adaptive system,
- co-evolutionary,
- Markov process,
- agent's behavior,
- invariable distribution,
- game theory
Citation: Hebing Zhang, Xiaojing Zheng. Invariable distribution of co-evolutionary complex adaptive systems with agent's behavior and local topological configuration[J]. Mathematical Biosciences and Engineering, 2024, 21(2): 3229-3261. doi: 10.3934/mbe.2024143

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Abstract

In this study, we developed a dynamical Multi-Local-Worlds (MLW) complex adaptive system with co-evolution of agent's behavior and local topological configuration to predict whether agents' behavior would converge to a certain invariable distribution and derive the conditions that should be satisfied by the invariable distribution of the optimal strategies in a dynamical system structure. To this end, a Markov process controlled by agent's behavior and local graphic topology configuration was constructed to describe the dynamic case's interaction property. After analysis, the invariable distribution of the system was obtained using the stochastic process method. Then, three kinds of agent's behavior (smart, normal, and irrational) coupled with corresponding behaviors, were introduced as an example to prove that their strategies converge to a certain invariable distribution. The results showed that an agent selected his/her behavior according to the evolution of random complex networks driven by preferential attachment and a volatility mechanism with its payment, which made the complex adaptive system evolve. We conclude that the corresponding invariable distribution was determined by agent's behavior, the system's topology configuration, the agent's behavior noise, and the system population. The invariable distribution with agent's behavior noise tending to zero differed from that with the population tending to infinity. The universal conclusion, corresponding to the properties of both dynamical MLW complex adaptive system and cooperative/non-cooperative game that are much closer to the common property of actual economic and management events that have not been analyzed before, is instrumental in substantiating managers' decision-making in the development of traffic systems, urban models, industrial clusters, technology innovation centers, and other applications.

References

[1]	M. A. Fuentes, A. Gerig, J. Vicente, Universal behavior of extreme price movements in stock markets, PLoS ONE, 4 (2009), e8243. https://doi.org/10.1371/journal.pone.0008243 doi: 10.1371/journal.pone.0008243
[2]	M. T. J. Heino, K. Knittle, C. Noone, F. Hasselman, N. Hankonen, Studying behaviour change mechanisms under complexity, Behav. Sci., 11 (2021), 1–22. https://doi.org/10.3390/bs11050077 doi: 10.3390/bs11050077
[3]	S. Bowles, E. A. Smith, M. B. Mulder, The Emergence and Persistence of Inequality in Premodern Societies Introduction to the Special Section, Curr. Anthropol., 51 (2010), 7–17. https://doi.org/10.1086/649206 doi: 10.1086/649206
[4]	S. Bartolucci, F. Caccioli, P. Vivo, A percolation model for the emergence of the Bitcoin Lightning Network, Sci. Rep.-UK, 10 (2020), 4488. https://doi.org/10.1038/s41598-020-61137-5 doi: 10.1038/s41598-020-61137-5
[5]	C. Hesp, M. Ramstead, A. Constant, P. Badcock, M. Kirchhoff, K. Friston, A multi-scale view of the emergent complexity of life: A free-energy proposal, in Evolution, Development and Complexity. Springer Proceedings in Complexity, (eds G. Georgiev, J. Smart, C. Flores Martinez, M. Price), Springer, Cham, (2019), 195–227. https://doi.org/10.1007/978-3-030-00075-2_7
[6]	J. P. Bagrow, D. Wang, A. L Barabasi, Collective response of human populations to large-scale emergencies, PLoS One, 6 (2011), e17680. https://doi.org/10.1371/journal.pone.0017680 doi: 10.1371/journal.pone.0017680
[7]	E. I. Badano, P. A. Marquet, L. A. Cavieres, Predicting effects of ecosystem engineering on species richness along primary productivity gradients, Acta. Oecol., 36 (2010), 46–54. https://doi.org/10.1016/j.actao.2009.09.008 doi: 10.1016/j.actao.2009.09.008
[8]	F. Brauer, Z. L. Feng, C. Castillo-Chavez, Discrete epidemic models, Math. Biosci. Eng., 7 (2010), 1–15. https://doi.org/10.3934/mbe.2010.7.1 doi: 10.3934/mbe.2010.7.1
[9]	S. E. Kreps, D. L. Kriner, Model uncertainty, political contestation, and public trust in science: Evidence from the COVID-19 pandemic, Sci. Adv., 6 (2020), eabd4563. https://doi.org/10.1126/sciadv.abd4563 doi: 10.1126/sciadv.abd4563
[10]	G. F. D. Arruda, L. G. S. Jeub, A. S. Mata, F. A. Rodrigues, Y. Moreno, From subcritical behavior to elusive transition in rumor models, Nat. Commun., 13 (2022), 3049. https://doi.org/10.1038/s41467-022-30683-z doi: 10.1038/s41467-022-30683-z
[11]	J. Andreoni, N. Nikiforakis, S. Siegenthaler, Predicting social tipping and norm change in controlled experiments, P. Natl. A. Sci., 118 (2021), 2014893118. https://doi.org/10.1073/pnas.2014893118 doi: 10.1073/pnas.2014893118
[12]	I. Kozic, Role of symmetry in irrational choice, preprint, arXiv: 1806.02627[physics.pop-ph].
[13]	R. M. D'Souza, M. di Bernardo, Y. Y. Liu, Controlling complex networks with complex nodes, Nat. Rev. Phys., 5 (2023), 250–262. https://doi.org/10.1038/s42254-023-00566-3 doi: 10.1038/s42254-023-00566-3
[14]	J. Li, C. Xia, G. Xiao, Y. Moreno, Crash dynamics of interdependent networks, Sci. Rep.-UK, 9 (2019), 14574. https://doi.org/10.1038/s41598-019-51030-1 doi: 10.1038/s41598-019-51030-1
[15]	N. Biderman, D. Shohamy, Memory and decision making interact to shape the value of unchosen options, Nat. Commun., 12 (2021), 4648. https://doi.org/10.1038/s41467-021-24907-x doi: 10.1038/s41467-021-24907-x
[16]	P. Rizkallah, A. Sarracino, Microscopic theory for the diffusion of an active particle in a crowded environment, Phys. Rev. Lett., 128 (2022), 038001. https://doi.org/10.1103/PhysRevLett.128.038001 doi: 10.1103/PhysRevLett.128.038001
[17]	D. Fernex, B. R. Noack, R Semaan, Cluster-based network modeling—From snapshots to complex dynamical systems, Sci. Adv., 7 (2021), eabf5006. https://doi.org/10.1126/SCIADV.ABF5006 doi: 10.1126/SCIADV.ABF5006
[18]	L. Gavassino, M. Antonelli, B. Haskell, Thermodynamic stability implies causality, Phyl. Rev. Lett., 128 (2021), 010606. https://doi.org/10.48550/arXiv.2105.14621 doi: 10.48550/arXiv.2105.14621
[19]	P. Cardaliaguet, C. Rainer, Stochastic differential games with asymmetric information, Appl. Math. Opt., 59(2009), 1–36. https://doi.org/10.1007/s00245-008-9042-0 doi: 10.1007/s00245-008-9042-0
[20]	P. Mertikopoulos, A. L. Moustakas, The emergence of rational behavior in the presence of stochastic perturbations, Ann. Appl. Probab., 20 (2010), 1359–1388. https://doi.org/10.1214/09-AAP651 doi: 10.1214/09-AAP651
[21]	I. Durham, A formal model for adaptive free choice in complex systems, Entropy, 22 (2020), 568. https://doi.org/10.3390/e22050568 doi: 10.3390/e22050568
[22]	R. Atar, A. Budhiraja, On near optimal trajectories for a game associated with the ∞-Laplacian, Probab. Theory. Rel., 151(2011), 509–528. https://doi.org/10.1007/s00440-010-0306-7 doi: 10.1007/s00440-010-0306-7
[23]	W. Brian, Foundations of complexity economics, Nat. Rev. Phys., 3 (2021), 136–145. https://doi.org/10.1038/s42254-020-00273-3 doi: 10.1038/s42254-020-00273-3
[24]	J. H. Jiang, K. Ranabhat, X. Y. Wang, Active transformations of topological structures in light-driven nematic disclination networks, P. Natl. Acad. Sci., 119 (2022), 2122226119. https://doi.org/10.1073/pnas.2122226119 doi: 10.1073/pnas.2122226119
[25]	H. P Maia, S. C Ferreira, M. L Martins, Adaptive network approach for emergence of societal bubbles, Phys. A, 572 (2021), 125588. https://doi.org/10.1016/j.physa.2020.125588 doi: 10.1016/j.physa.2020.125588
[26]	W. Zou, D. V. Senthikumar, M. Zhan, J. Kurths, Quenching, aging, and reviving in coupled dynamical networks, Phys. Rep., 931 (2021), 1–72. https://doi.org/10.1016/j.physrep.2021.07.004 doi: 10.1016/j.physrep.2021.07.004
[27]	Z. Fulker, P. Forber, R. Smead, C. Riedl, Spite is contagious in dynamic networks, Nat. Commun., 12 (2021), 1–9. https://doi.org/10.1038/s41467-020-20436-1 doi: 10.1038/s41467-020-20436-1
[28]	M. Colnaghi, F. P. Santos, P. A. M. V. Lange, D. Balliet, Adaptations to infer fitness interdependence promote the evolution of cooperation. P. Natl. Acad. Sci. USA, 120 (2023). https://doi.org/10.1073/pnas.2312242120
[29]	S. Carozza, D. Akarca, D. Astle, The adaptive stochasticity hypothesis: Modeling equifinality, multifinality, and adaptation to adversity, P. Natl. Acad. Sci. USA, 120 (2023). https://doi.org/10.1073/pnas.2307508120
[30]	R. Berner, S. Vock, E. Schöll, S. Yanchuk, Desynchronization transitions in adaptive networks, Phys. Rev. Lett., 126 (2021), 028301. https://doi.org/10.1103/PhysRevLett.126.028301 doi: 10.1103/PhysRevLett.126.028301
[31]	M. C. Miguel, J. T. Parley, R. Pastor-Satorras, Effects of heterogeneous social interactions on flocking dynamics Phys. Rev. Lett., 120 (2018), 068303. https://doi.org/10.1103/PhysRevLett.120.068303
[32]	T. Hassler, J. Ullrich, M. Bernardino, N. Shnabel, C. V. Laar, D. Valdenegro, et.al., A large-scale test of the link between intergroup contact and support for social change, Nat. Hum. Behav., 4 (2020), 380–386. https://doi.org/10.1038/s41562-019-0815-z doi: 10.1038/s41562-019-0815-z
[33]	P. DeLellis, M. D. Bemardo, T. E. Gorochowski, G. Russo, Synchronization and control of complex networks via contraction, adaptation and evolution, IEEE Circ. Syst. Mag., 10 (2010), 64–82. https://doi.org/10.1109/MCAS.2010.937884
[34]	F. M. Neffke, The value of complementary co-workers, Sci. Adv., 5 (2019), eaax3370. https://doi.org/10.1126/sciadv.aax3370 doi: 10.1126/sciadv.aax3370
[35]	S. A. Levin, H. V. Milner, C. Perrings, The dynamics of political polarization, P. Natl. Acad. Sci. USA, 118 (2021), e2116950118. https://doi.org/10.1073/pnas.2116950118 doi: 10.1073/pnas.2116950118
[36]	C. Le Priol, P. Le Doussal, A. Rosso, Spatial clustering of depinning avalanches in presence of long-range interactions, Phys. Rev. Lett., 126 (2021), 025702. https://doi.org/10.1103/PhysRevLett.126.025702 doi: 10.1103/PhysRevLett.126.025702
[37]	M. Pirani, S. Baldi, K. H. Johansson, Impact of network topology on the resilience of vehicle platoons, IEEE T. Intell. Transp., 23 (2022), 15166–15177. https://doi.org/10.1109/TITS.2021.3137826 doi: 10.1109/TITS.2021.3137826
[38]	T. Narizuka, Y. Yoshihiro, Lifetime distributions for adjacency relationships in a vicsek Yamazaki model, Phys. Rev. E, 100 (2019), 032603. https://doi.org/10.1103/PhysRevE.100.032603 doi: 10.1103/PhysRevE.100.032603
[39]	L. Tiokhin, M. Yan, T. J. Morgan, Competition for priority harms the reliability of science, but reforms can help, Nat. Hum. Behav., 5 (2021), 857–867. https://doi.org/10.1038/s41562-020-01040-1
[40]	R. K. Colwell, Spatial scale and the synchrony of ecological disruption, Nature, 599 (2021), E8–E10. https://doi.org/10.1038/s41586-021-03759-x doi: 10.1038/s41586-021-03759-x
[41]	J. E. Allgeier, T. J. Cline, T. E. Walsworth, G. Wathen, C. A. Layman, D. E. Schindler, Individual behavior drives ecosystem function and the impacts of harvest, Sci. Adv., 6 (2020), eaax8329. https://doi.org/10.1126/sciadv.aax8329 doi: 10.1126/sciadv.aax8329
[42]	B. J. Tóth, G. Palla, E. Mones, G. Havadi, N. Pall, P. Pollner, T. Vicsek, Emergence of leader-follower hierarchy among players in an on-line experiment, in 2018 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), (IEEE), (2018), 1184–1190. https://doi.org/10.1109/ASONAM.2018.8508278
[43]	A. N. Tump, T. J. Pleskac, R. H. Kurvers, Wise or mad crowds? The cognitive mechanisms underlying information cascades, Sci. Adv., 6 (2020), eabb0266. https://doi.org/10.1126/sciadv.abb0266 doi: 10.1126/sciadv.abb0266
[44]	R. Berner, S. Vock, E. Schöll, S. Yanchuk, Desynchronization transitions in adaptive networks, Phys. Rev. Lett., 126 (2021), 028301. https://doi.org/10.1103/physrevlett.126.028301 doi: 10.1103/physrevlett.126.028301
[45]	L. Zhang, W. Chen, M. Antony, K. Y. Szeto, Phase diagram of symmetric iterated prisoner's dilemma of two companies with partial imitation rule. preprint, arXiv: 1103.6103[physics.soc-ph].
[46]	G. Chen, Small noise may diversify collective motion in Vicsek model, IEEE T. Automat. Contr., 62 (2016), 636–651. https://doi.org/10.1109/tac.2016.2560144 doi: 10.1109/tac.2016.2560144
[47]	M. Staudigi, Co-evolutionary dynamics and Bayesian interaction games, Int. J. Game Theory, 42 (2013), 179–210. https://doi.org/10.1007/s00182-012-0331-0 doi: 10.1007/s00182-012-0331-0

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