The problem of identifying the sources of switching in the dynamics of nonlinear coupled systems and their mathematical prediction is considered. We study a metapopulation system formed by two oscillating subpopulations coupled by mutual migration. For this model, parametric zones of mono-, bi-, and tri-rhythmicity with the coexistence of regular and chaotic attractors are revealed. The effects of random perturbations in the migration intensity parameter are studied both by methods of statistical analysis of the results of direct numerical simulation and by using the analytical technique of stochastic sensitivity. Noise-induced transitions between anti- and in-phase synchronization modes, as well as between order and chaos, are being studied. Here, the role of transient chaotic attractors and their fractal basins is discussed.
REFERENCES
1.
A.
Pikovski
, M.
Rosenblum
, and J.
Kurths
, Synchronization: A Universal Concept in Nonlinear Sciences
(Cambridge University Press
, Cambridge
, 2001
).2.
S.
Boccaletti
, A. N.
Pisarchik
, C. I.
del Genio
, and A.
Amann
, Synchronization: From Coupled Systems to Complex Networks
(Cambridge University Press
, 2018
).3.
G.
Nicolis
and I.
Prigogine
, Self-Organization in Nonequilibrium Systems
(Wiley
, New York
, 1977
).4.
M.
Cross
and H.
Greenside
, Pattern Formation and Dynamics in Nonequilibrium Systems
(Cambridge University Press
, Cambridge
, 2009
).5.
Y.
Kuramoto
and D.
Battogtokh
, “Coexistence of coherence and incoherence in nonlocally coupled phase oscillators
,” Nonlinear Phenom. Complex Syst.
5
, 380
–385
(2002
).6.
M. J.
Panaggio
and D. M.
Abrams
, “Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
,” Nonlinearity
28
(3
), R67
–R87
(2015
). 7.
A.
Zakharova
, Chimera Patterns in Complex Networks
(Springer
, Berlin
, 2020
).8.
R.
May
, “Simple mathematical models with very complicated dynamics
,” Nature
261
, 459
–467
(1976
). 9.
H.
Sakaguchi
and K.
Tomita
, “Bifurcations of the coupled logistic map
,” Prog. Theor. Phys.
78
(2
), 305
–315
(1987
). 10.
Yu. L.
Maistrenko
, V. L.
Maistrenko
, A.
Popovich
, and E.
Mosekilde
, “Transverse instability and riddled basins in a system of two coupled logistic maps
,” Phys. Rev. E
57
, 2713
–2724
(1998
). 11.
G.
Tanaka
, M. A. F.
Sanjuán
, and K.
Aihara
, “Crisis-induced intermittency in two coupled chaotic maps: Towards understanding chaotic itinerancy
,” Phys. Rev. E
71
, 016219
(2005
). 12.
I.
Bashkirtseva
and L.
Ryashko
, “Chaotic transients, riddled basins, and stochastic transitions in coupled periodic logistic maps
,” Chaos
31
, 053101
(2021
). 13.
Z. T.
Zhusubaliyev
and E.
Mosekilde
, “Multilayered tori in a system of two coupled logistic maps
,” Phys. Lett. A
373
(10
), 946
–951
(2009
). 14.
R.
Lande
, S.
Engen
, and B.-E.
Saether
, Stochastic Population Dynamics in Ecology and Conservation
(Oxford University Press
, Oxford
, 2003
).15.
J. V.
Greenman
and T. G.
Benton
, “The impact of environmental fluctuations on structured discrete time population models: Resonance, synchrony and threshold behaviour
,” Theor. Popul. Biol.
68
(4
), 217
–235
(2005
). 16.
17.
V. S.
Anishchenko
, V. V.
Astakhov
, A. B.
Neiman
, T. E.
Vadivasova
, and L.
Schimansky-Geier
, Nonlinear Dynamics of Chaotic and Stochastic Systems. Tutorial and Modern Development
(Springer-Verlag
, Berlin
, 2007
).18.
S.
Kraut
and U.
Feudel
, “Multistability, noise, and attractor hopping: The crucial role of chaotic saddles
,” Phys. Rev. E
66
, 015207
(2002
). 19.
W.
Lin
and G.
Chen
, “Using white noise to enhance synchronization of coupled chaotic systems
,” Chaos
16
, 013134
(2006
). 20.
Y.
Sun
and D.
Zhao
, “Effects of noise on the outer synchronization of two unidirectionally coupled complex dynamical networks
,” Chaos
22
, 023131
(2012
). 21.
Y.
Zhang
, Z. G.
Nicolaou
, J. D.
Hart
, R.
Roy
, and A. E.
Motter
, “Critical switching in globally attractive chimeras
,” Phys. Rev. X
10
, 011044
(2020
). 22.
I.
Bashkirtseva
, L.
Ryashko
, and A. N.
Pisarchik
, “Stochastic transitions between in-phase and anti-phase synchronization in coupled map-based neural oscillators
,” Commun. Nonlinear Sci. Numer. Simul.
95
, 105611
(2021
). 23.
E. V.
Rybalova
, T. E.
Vadivasova
, G. I.
Strelkova
, and A.
Zakharova
, “Multiplexing noise induces synchronization in multilayer networks
,” Chaos, Solitons Fractals
163
, 112521
(2022
). 24.
I.
Bashkirtseva
, L.
Ryashko
, and I.
Tsvetkov
, “Sensitivity analysis of stochastic equilibria and cycles for the discrete dynamic systems
,” Dyn. Contin. Discrete Impuls. Syst. Ser. A: Math. Anal.
17
, 501
–515
(2010
).25.
I.
Bashkirtseva
and L.
Ryashko
, “Stochastic sensitivity analysis of noise-induced phenomena in discrete systems,” in Recent Trends in Chaotic, Nonlinear and Complex Dynamics, World Scientific Series on Nonlinear Science Series B (World Scientific, 2021), Chap. 8, pp. 173–192.26.
I.
Bashkirtseva
and L.
Ryashko
, “Stochastic sensitivity of regular and multi-band chaotic attractors in discrete systems with parametric noise
,” Phys. Lett. A
381
(37
), 3203
–3210
(2017
). 27.
L.
Ryashko
, “Sensitivity analysis of the noise-induced oscillatory multistability in Higgins model of glycolysis
,” Chaos
28
(3
), 033602
(2018
). 28.
D. V.
Alexandrov
, I. A.
Bashkirtseva
, M.
Crucifix
, and L. B.
Ryashko
, “Nonlinear climate dynamics: From deterministic behaviour to stochastic excitability and chaos
,” Phys. Rep.
902
, 1
–60
(2021
). 29.
W. E.
Ricker
, “Stock and recruitment
,” J. Fish. Res. Board Can.
11
, 559
–623
(1954
). 30.
T. J.
Quinn
and R. B.
Deriso
, Quantitative Fish Dynamics
(Oxford University Press
, Oxford
, 1999
).31.
E. P.
Bjorkstedt
, “Ricker model,” in Encyclopedia of Theoretical Ecology (University of California Press, Berkeley, CA, 2012), pp. 632–636.32.
I.
Bashkirtseva
and L.
Ryashko
, “Stochastic sensitivity analysis of noise-induced extinction in the Ricker model with delay and Allee effect
,” Bull. Math. Biol.
80
(6
), 1596
–1614
(2018
). 33.
Y.-C.
Lai
and T.
Tel
, Transient Chaos. Complex Dynamics on Finite Time Scales
(Springer-Verlag
, New York
, 2011
).34.
I.
Bashkirtseva
and L.
Ryashko
, “Stochastic sensitivity of the closed invariant curves for discrete-time systems
,” Physica A
410
, 236
–243
(2014
). 35.
I.
Bashkirtseva
and L.
Ryashko
, “Stochastic sensitivity analysis of chaotic attractors in 2D non-invertible maps
,” Chaos, Solitons Fractals
126
, 78
–84
(2019
). 36.
G. N.
Mil’shtein
and L. B.
Ryashko
, “A first approximation of the quasipotential in problems of the stability of systems with random non-degenerate perturbations
,” J. Appl. Math. Mech.
59
(1
), 47
–56
(1995
). 37.
M. I.
Freidlin
and A. D.
Wentzell
, Random Perturbations of Dynamical Systems
(Springer
, Berlin
, 2012
).38.
I.
Bashkirtseva
, L.
Ryashko
, and G.
Chen
, “Controlling the equilibria of nonlinear stochastic systems based on noisy data
,” J. Franklin Inst.
354
(3
), 1658
–1672
(2017
). 39.
I.
Bashkirtseva
, L.
Ryashko
, and G.
Chen
, “Stochastic sensitivity synthesis in nonlinear systems with incomplete information
,” J. Franklin Inst.
357
(9
), 5187
–5198
(2020
). 40.
K.
Garain
and P.
Sarathi Mandal
, “Stochastic sensitivity analysis and early warning signals of critical transitions in a tri-stable prey-predator system with noise
,” Chaos
32
(3
), 033115
(2022
). 41.
E.
Slepukhina
, I.
Bashkirtseva
, P.
Kügler
, and L.
Ryashko
, “Noise-driven bursting birhythmicity in the Hindmarsh–Rose neuron model
,” Chaos
33
(3
), 033106
(2023
). 42.
M.
Huang
, A.
Yang
, S.
Yuan
, and T.
Zhang
, “Stochastic sensitivity analysis and feedback control of noise-induced transitions in a predator-prey model with anti-predator behavior
,” Math. Biosci. Eng.
20
(2
), 4219
–4242
(2023
). © 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
