Double time-delays induced stochastic dynamical characteristics for a metapopulation system subjected to the associated noises and a multiplicative periodic signal. (English) Zbl 1380.92060
Summary: In this paper, we aim to investigating in detail the stability of the system, the mean extinction time and stochastic resonance (SR) phenomena caused by a multiplicative periodic signal for a dual time-delayed metapopulation system subjected to cross-correlated noises. By use of the fast descent method, the small time delay approximation method and the SR theory, we obtain the expressions of the steady state probability distribution function, the mean first-passage time and signal-to-noise ratio (SNR). Numerical results indicate that the multiplicative, additive and association noises together with time delay \(\tau\) can all accelerate the transition from the stable state of big density to the extinction one and play significant roles in weakening the stability and shortening the mean extinction time of the metapopulation. In particular, the additive noise and time delay \(\tau\) can result in the crash of the system, while another time delay \(\theta\) can strengthen the biological system stability and extend the declining time for the population. On the other hand, with respect to the SNR, the figures show that time delay \(\tau\) plays entirely antipodal roles in motivating stochastic resonance (SR) in a variety of different situations. Conversely, the multiplicative noise intensity \(Q\) and time delay \(\theta\) all along produce negative effect on exciting the SR. Meanwhile, the increase of the weak additive noise intensity \(M\) can stimulate the SR phenomenon, but the bigger values of M will suppress the SNR and SR phenomenon. The strength of the noise correlation \(\lambda\) plays an important role in restraining the SR in most cases except that it does in the plot of SNR-\(Q\).
MSC:
92D25 | Population dynamics (general) |
34F15 | Resonance phenomena for ordinary differential equations involving randomness |
60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
metapopulation system; mean extinction time; signal-to-noise ratio; stochastic resonance; double time delayReferences:
[1] | Gammaitoni, L.; Hänggi, P.; Jung, P.; Marchesoni, F., Rev Mod Phys, 70, 233 (1998) |
[2] | Benzi, R.; Sutera, A.; Vulpiani, A., J Phys A: Math Gen, 14, L453 (1981) |
[3] | Nicolis, C., Tellus, 34, 1 (1982) |
[4] | McNamara, B.; Wiensenfeld, K., Phys Rev A, 39, 4854 (1989) |
[5] | Jung, P.; Hänggi, P., Phys Rev A, 44, 8032 (1991) |
[6] | Jung, P., Phys Rep, 234, 175 (1993) |
[7] | Hänggi, P.; Inchiosa, M. E.; Fogliatti, D.; Bulsara, A. R., Phys Rev E, 62, 6155 (2000) |
[8] | Loerincz, K.; Gingl, Z.; Kiss, L. B., Phys Lett A, 224, 63 (1996) |
[9] | Gingl, Z.; Makra, P.; Vajtai, R., Fluct Noise Lett, 1, L181 (2001) |
[10] | Chapeau-Blondeau, F.; Godivier, X., Phys Rev.E, 55, 1478 (1997) |
[11] | Chapeau-Blondeau, F.; Rousseau, D., Phys Rev E, 70, Article 060101 pp. (2004), (R) |
[12] | Chapeau-Blondeau, F.; Rousseau, D., Phys Lett A, 351, 231 (2006) |
[13] | Casado-Pascual, J.; Gómez-Ordóñez, J.; Morillo, M., Phys Rev Lett, 91, Article 210601 pp. (2003) |
[14] | Casado-Pascual, J.; Denk, C.; Gómez-Ordóñez, J.; Morillo, M., Phys Rev E, 67, Article 036109 pp. (2003) |
[15] | Casado-Pascual, J.; Gómez-Ordóñez, J.; Morillo, M.; Hänggi, P., Phys Rev E, 68, Article 061104 pp. (2003) |
[16] | Casado, J. M.; Gómez-Ordóñez, J.; Morillo, M., Phys Rev E, 73, Article 011109 pp. (2006) |
[17] | Dykman, M. I.; McClintock, P. V.E., Nature, 391, 344 (1998) |
[18] | Neiman, A.; Schimansky-Geier, L.; Moss, F., Phys Rev E, 56, R9 (1997) |
[19] | Duan, F.; Chapeau-Blondeau, F.; Abbott, D., Electron Lett, 42, 1008 (2006) |
[20] | Duan, F. B.; Chapeau-Blondeau, F.; Abbott, D., Phys Lett A, 372, 2159 (2008) · Zbl 1220.60025 |
[21] | Bechhoefer, J., Rev Mod Phys, 77, 783 (2005) |
[22] | Ikeda, K.; Kondo, K.; Akimoto, O., Phys Rev Lett, 49, 1467 (1982) |
[23] | Van Wiggeren, G. D.; Roy, R., Science, 279, 1198 (1998) |
[24] | Socolar, J. E.S.; Sukow, D. W.; Gauthier, D. J., Phys Rev E, 50, 3245 (1994) |
[25] | Epstein, I. R., Int Rev Phys Chem, 11, 135 (1992) |
[26] | Pakdaman, K.; Vibert, J. F.; Boussard, E.; Azmy, N., Neural Networks, 9, 797 (1996) |
[27] | Gerstner, W., Phys Rev Lett, 76, 1755 (1996) |
[28] | Marcus, C. M.; Westerwelt, R. M., Phys Rev A, 39, 347 (1989) |
[29] | Yang, J. Y.; Sanjuán Miguel, A. F.; Liu, H. G.; Zhu, H., Nonlinear Dyn., 87, 3, 1721-1730 (2017) |
[30] | Yang, J. H.; Sanjuán Miguel, A. F.; Liu, H. G.; Litak, G.; Li, X., Commun. Nonlinear Sci. Numer. Simul., 41, 104-117 (2016) · Zbl 1458.34108 |
[31] | Pyragas, K., Phys. Lett. A, 170, 421 (1992) |
[32] | Voss, H. U., Phys Rev Lett, 87, Article 014102 pp. (2001) |
[33] | Longtin, A.; Milton, J. G.; Bos, J. E.; Mackey, M. C.., Phys Rev A, 41, 6992 (1990) |
[34] | Gammaitoni, L.; Hänggi, P.; Jung, P.; Marchesoni, F., Rev Mod Phys, 70, 223 (1998) |
[35] | Pikovsky, A.; Kurths, J., Phys Rev Lett, 78, 775 (1997) · Zbl 0961.70506 |
[36] | Jung, P., Phys Rev E, 50, 2513 (1994) |
[37] | Gingl, Z.; Kiss, L. B.; Moss, F., Nuovo Cimento D, 17, 795 (1995) |
[38] | Godivier, X.; Chapeau-Blondeau, F., Europhys Lett, 35, 473 (1996) |
[39] | Stocks, N., Phys Rev Lett, 84, 2310 (2000) |
[40] | Yang, J. H.; Sanjuán Miguel, A. F.; Liu, H. G., Commun. Nonlinear Sci. Numer. Simul., 22, 1-3, 1158-1168 (2015) |
[41] | Kim, S.; Park, S. H.; Pyo, H.-B., Phys Rev Lett, 82, 1620 (1999) |
[42] | Ohira, T.; Sato, Y., Phys Rev Lett, 82, 2811 (1999) |
[43] | Morse, R.; Longtin, A., Phys Lett A, 359, 640 (2006) |
[44] | Levins Bull, R., Entomol Soc Am, 15, 237 (1998) |
[45] | Levins Lect, R., Notes Math, 2, 75 (1970) |
[46] | Moilanen, A.; Hanski, I., Ecology, 79, 2503 (1998) |
[47] | Hastings, A.; Harrison, S., Ann Rev Ecol Syst, 25, 167 (1994) |
[48] | Novikov Sov, EA, Phys JETP, 20, 1290 (1964) |
[49] | Fox, RF, Phys Rev A, 34, 4525 (1986) |
[50] | Zeng, C. H.; Han, Q. L.; Yang, T.; Wang, H.; Jia, Z. L., J Stat Mech, P10017 (2013) |
[51] | McNamara, B.; Wiesenfeld, K., Phys Rev A, 39, 4854 (1989) |
[52] | Fiasconaro, A.; Spagnolo, B.; Boccaletti, S., Phys Rev E, 72, Article 061110 pp. (2005) |
[53] | Spagnolo, B.; Dubkov, A. A.; Agudov, N. V., Eur Phys J B, 40, 273-281 (2004) |
[54] | Mantegna, R. N.; Spagnolo, B., Int J Bif and Chaos, 8, 783-790 (1998) · Zbl 0936.82037 |
[55] | Fiasconaro, A.; Mazo, J. J.; Spagnolo, B., Phys Rev E, 82, Article 041120 pp. (2010) |
[56] | Agudov, N. V.; Dubkov, A. A.; Spagnolo, B., Physica A, 325, 144-151 (2003) · Zbl 1029.82029 |
[57] | Agudov, N. V.; Krichigin, A. V.; Valenti, D.; Spagnolo, B., Phys Rev E, 81, Article 051123 pp. (2010) |
[58] | Mantegna, R. N.; Spagnolo, B.; Testa, L.; Trapanese, M., J Appl Phys, 97, 10E519 (2005) |
[59] | Ciuchi, S.; De, P. F.; Spagnolo, B., Phys Rev E, 47, 3915-3926 (1993) |
[60] | Caruso, A.; Gargano, M. E.; Valenti, D.; Fiasconaro, A.; Spagnolo, B., Fluct Noise Lett, 3, L177-L185 (2003) |
[61] | Pankratov, A. L., Phys Lett A, 234, 329-335 (1997) · Zbl 0967.82504 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.