Transient behaviour near an instability point: Vectorial stochastic representation of the Malthus-Verhulst model
作者： F. de Pasquale , P. Tartaglia , P. Tombesi
DOI: 10.1007/BF02721268
关键词: Physics 、 Integer 、 State (functional analysis) 、 Stochastic process 、 Transient (oscillation) 、 Analytic continuation 、 Instability 、 Statistical physics 、 Representation (mathematics) 、 Population
摘要: We study the fluctuations in Malthus-Verhulst model of population dynamics vicinity instability point. introduce a representation terms an-dimensional simple stochastic process, wheren is an integer related to rate parameters model. are thus able obtain transient behaviour for decay from unstable state by means quasi-deterministic approximation. Forn=1 and 2 we recover well-known case double-well potential single-mode laser, respectively. show that it also possible perform analytic continuation results any noninteger positiven.
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sci-hub.se 参考文章(15)
F. Schl�gl, Chemical reaction models for non-equilibrium phase transitions European Physical Journal. ,vol. 253, pp. 147- 161 ,(1972) , 10.1007/BF01379769
F. de Pasquale, P. Tombesi, The decay of an unstable equilibrium state near a “critical point” Physics Letters A. ,vol. 72, pp. 7- 9 ,(1979) , 10.1016/0375-9601(79)90509-7
F. de Pasquale, P. Tartaglia, P. Tombesi, Stochastic approach to chemical instabilities: Anomalous fluctuation and transient behaviour Lettere Al Nuovo Cimento. ,vol. 28, pp. 141- 145 ,(1980) , 10.1007/BF02772919
N. J. Rao, J. D. Borwanker, D. Ramkrishna, Numerical Solution of Ito Integral Equations Siam Journal on Control. ,vol. 12, pp. 124- 139 ,(1974) , 10.1137/0312011
H. K. Janssen, On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state European Physical Journal B. ,vol. 42, pp. 151- 154 ,(1981) , 10.1007/BF01319549
S. Chaturvedi, C.W. Gardiner, D.F. Walls, Exact Fokker-Planck equations from stochastic master equations Physics Letters A. ,vol. 57, pp. 404- 406 ,(1976) , 10.1016/0375-9601(76)90104-3
P. Grassberger, K. Sundermeyer, Reggeon field theory and markov processes Physics Letters B. ,vol. 77, pp. 220- 222 ,(1978) , 10.1016/0370-2693(78)90626-3
F. de Pasquale, P. Tartaglia, P. Tombesi, Transient behavior of nonequilibrium phase transitions Physics Letters A. ,vol. 78, pp. 129- 132 ,(1980) , 10.1016/0375-9601(80)90675-1
G. Dewel, D. Walgraef, P. Borckmans, Renormalization group approach to chemical instabilities Zeitschrift f�r Physik B Condensed Matter and Quanta. ,vol. 28, pp. 235- 237 ,(1977) , 10.1007/BF01313046
Isaac Goldhirsch, Itamar Procaccia, Nonlinear behavior at a chemical instability: A detailed renormalization-group analysis of a case model Physical Review A. ,vol. 24, pp. 572- 579 ,(1981) , 10.1103/PHYSREVA.24.572