Complex network near-synchronization for non-identical predator-prey systems

Guillaume Cantin; Cristiana J. Silva; Guillaume Cantin; Cristiana J. Silva

doi:10.3934/math.20221093

AIMS Mathematics

2022, Volume 7, Issue 11: 19975-19997. doi: 10.3934/math.20221093

Previous Article Next Article

Research article Special Issues

Complex network near-synchronization for non-identical predator-prey systems

Guillaume Cantin ^{1
,},
Cristiana J. Silva ^{2,3
,
,}

1.
Laboratoire des Sciences du Numérique de Nantes, Nantes Université, CNRS UMR 6004, France; guillaume.cantin@univ-nantes.fr
2.
Instituto Universitário de Lisboa (ISCTE-IUL), Av. das Forças Armadas, 1649-026, Lisbon, Portugal
3.
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Received: 04 July 2022 Revised: 28 August 2022 Accepted: 07 September 2022 Published: 13 September 2022
MSC : 34A34, 34C60, 92B05

In this paper, we analyze the properties of a complex network of predator-prey systems, modeling the ecological dynamics of interacting species living in a fragmented environment. We consider non-identical instances of a Lotka-Volterra model with Holling type II functional response, which undergoes a Hopf bifurcation, and focus on the possible synchronization of distinct local behaviours. We prove an original result for the near-synchronization of non-identical systems, which shows how to and to what extent an extinction dynamic can be driven to a persistence equilibrium. Our theoretical statements are illustrated by appropriate numerical simulations.
- complex network,
- non-identical systems,
- synchronization,
- ecology
Citation: Guillaume Cantin, Cristiana J. Silva. Complex network near-synchronization for non-identical predator-prey systems[J]. AIMS Mathematics, 2022, 7(11): 19975-19997. doi: 10.3934/math.20221093

Related Papers:

Abstract

In this paper, we analyze the properties of a complex network of predator-prey systems, modeling the ecological dynamics of interacting species living in a fragmented environment. We consider non-identical instances of a Lotka-Volterra model with Holling type II functional response, which undergoes a Hopf bifurcation, and focus on the possible synchronization of distinct local behaviours. We prove an original result for the near-synchronization of non-identical systems, which shows how to and to what extent an extinction dynamic can be driven to a persistence equilibrium. Our theoretical statements are illustrated by appropriate numerical simulations.

References

[1]	A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Synchronization in complex networks, Physics reports, 469 (2008), 93–153. https://doi.org/10.1016/j.physrep.2008.09.002 doi: 10.1016/j.physrep.2008.09.002
[2]	M. Barahona, L. M. Pecora, Synchronization in small-world systems, Phys. rev. lett., 89 (2002), 054101. https://doi.org/10.1103/PhysRevLett.89.054101 doi: 10.1103/PhysRevLett.89.054101
[3]	D. Barman, J. Roy, S. Alam, Modelling hiding behaviour in a predator-prey system by both integer order and fractional order derivatives, Ecol. Inform., 67 (2022), 101483. https://doi.org/10.1016/j.ecoinf.2021.101483 doi: 10.1016/j.ecoinf.2021.101483
[4]	A. D. Bazykin, Nonlinear dynamics of interacting populations, World Scientific, 1998. https://doi.org/10.1142/2284
[5]	I. Belykh, M. Hasler, M. Lauret, H. Nijmeijer, Synchronization and graph topology, Int. J. Bifurcat. Chaos, 15 (2005), 3423–3433. https://doi.org/10.1142/S0218127405014143 doi: 10.1142/S0218127405014143
[6]	G. Cantin, M. Aziz-Alaoui, Dimension estimate of attractors for complex networks of reaction-diffusion systems applied to an ecological model, Commun. Pur. Appl. Anal., 20 (2021), 623. https://doi.org/10.3934/cpaa.2020283 doi: 10.3934/cpaa.2020283
[7]	R. Dirzo, H. S. Young, M. Galetti, G. Ceballos, N. J. Isaac, B. Collen, Defaunation in the Anthropocene, Science, 345 (2014), 401–406. https://doi.org/10.1126/science.1251817 doi: 10.1126/science.1251817
[8]	N. M. Haddad, L. A. Brudvig, J. Clobert, K. F. Davies, A. Gonzalez, R. D. Holt, et al., Habitat fragmentation and its lasting impact on earth's ecosystems, Sci. adv., 1 (2015), e1500052. https://doi.org/10.1126/sciadv.1500052 doi: 10.1126/sciadv.1500052
[9]	C. S. Holling, The functional response of predators to prey density and its role in mimicry and population regulation, The Memoirs of the Entomological Society of Canada, 97 (1965), 5–60. https://doi.org/10.4039/entm9745fv doi: 10.4039/entm9745fv
[10]	C. N. Johnson, A. Balmford, B. W. Brook, J. C. Buettel, M. Galetti, L. Guangchun, et al., Biodiversity losses and conservation responses in the Anthropocene, Science, 356 (2017), 270–275. https://doi.org/10.1126/science.aam9317 doi: 10.1126/science.aam9317
[11]	Y. A. Kuznetsov, I. A. Kuznetsov, Y. Kuznetsov, Elements of applied bifurcation theory, volume 112. Springer, 1998.
[12]	R. E. Leakey, R. Lewin, The sixth extinction: patterns of life and the future of humankind, J. Leisure Res., 29 (1997), 476. https://doi.org/10.1080/00222216.1997.11949812 doi: 10.1080/00222216.1997.11949812
[13]	B. J. McGill, M. Dornelas, N. J. Gotelli, A. E. Magurran, Fifteen forms of biodiversity trend in the Anthropocene, Trends ecol. evol., 30 (2015), 104–113. https://doi.org/10.1016/j.tree.2014.11.006 doi: 10.1016/j.tree.2014.11.006
[14]	A. Miranville, G. Cantin, M. Aziz-Alaoui, Bifurcations and synchronization in networks of unstable reaction–diffusion systems, J. Nonlinear Sci., 31 (2021), 1–34. https://doi.org/10.1007/s00332-021-09701-9 doi: 10.1007/s00332-021-09701-9
[15]	R. J. Naiman, H. Decamps, M. Pollock, The role of riparian corridors in maintaining regional biodiversity, Ecol. appl., 3 (1993), 209–212. https://doi.org/10.2307/1941822 doi: 10.2307/1941822
[16]	L. Perko, Differential equations and dynamical systems, volume 7, Springer Science & Business Media, 2013.
[17]	L. A. Real, The kinetics of functional response, The American Naturalist, 111 (1977), 289–300. https://doi.org/10.1086/283161 doi: 10.1086/283161
[18]	J. Roy, D. Barman, S. Alam, Role of fear in a predator-prey system with ratio-dependent functional response in deterministic and stochastic environment, Biosystems, 197 (2020), 104176. https://doi.org/10.1016/j.biosystems.2020.104176 doi: 10.1016/j.biosystems.2020.104176
[19]	G. T. Skalski, J. F. Gilliam, Functional responses with predator interference: viable alternatives to the holling type ii model, Ecology, 82 (2001), 3083–3092. https://doi.org/10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2 doi: 10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2
[20]	H. L. Smith, H. R. Thieme, Dynamical systems and population persistence, volume 118, American Mathematical Soc., 2011.
[21]	L. R. Tambosi, A. C. Martensen, M. C. Ribeiro, J. P. Metzger, A framework to optimize biodiversity restoration efforts based on habitat amount and landscape connectivity, Restor. ecol., 22 (2014), 169–177. https://doi.org/10.1111/rec.12049 doi: 10.1111/rec.12049
[22]	A. Yagi, Abstract parabolic evolution equations and their applications, Springer Science & Business Media, 2009. https://doi.org/10.1007/978-3-642-04631-5_4
[23]	R. Yang, C. Nie, D. Jin, Spatiotemporal dynamics induced by nonlocal competition in a diffusive predator-prey system with habitat complexity, Nonlinear Dynam., (2022), 1–22. https://doi.org/10.21203/rs.3.rs-1141642/v1
[24]	R. Yang, F. Wang, D. Jin, Spatially inhomogeneous bifurcating periodic solutions induced by nonlocal competition in a predator–prey system with additional food, Math. Method. Appl. Sci., (2022). https://doi.org/10.1002/mma.8349

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)