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A class of nonlinear system is studied. Firstly, the reaction-diffusion system with speed, temperature and humidity for a atmospheric nonlinear force dissipative system is discussed using the atmospheric nonlinear theory of thermodynamics and dynamics. Secondly, the small disturbed solution of atmospheric nonlinear reaction-diffusion system in the neighborhood of homogeneous steady state solution is obtained from the Lyapunov stability theory. Finally, from the variations of the control parameters for transgenic processes, the states of ordered-unordered-ordered processes of atmospheric nonlinear reaction-diffusion system are found. Thus the corresponding local atmospheric nonlinear force dissipative system can be predicated and calculated.
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Keywords:
- reaction-diffusion /
- thermodynamics /
- atmospheric nonlinear system
[1] Hu Y Q 2002 Introductory to Atmospheric Thermodynamics and Dynamics —Linear and Nonlinear Thermodynamics of the Atmospheric Non-equilibrium State (Being: Geology Publication) (in Chinese) [胡隐樵 2002 大气热力动力学导论——大气非平衡态线性和非线性热力学 (北京:地质出版社)]
[2] De Groot S K, Mazur P 1962 Non-equillbeium Thermodynamics (Amsterdam: North-Holland Pub. Co.)
[3] Prigogine I 1967 Introduction to Thermodynamics of Irreversible Processes (New York: Interscience Pub.)
[4] Shutts G J 1981 Quart. J. R. Met. So. 107 503
[5] Mhrt L 1986 J. Atmos. Sci. 43 1036
[6] de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation (Amsterdam: North- Holland Publishing Co.)
[7] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[8] Ramos M 2009 J. Math. Anal. Appl. 352 246
[9] D'Aprile T, Pistoia A 2010 J. Differ. Eqs. 248 556
[10] Faye L, Frenod E, Seck D 2011 Discrete Contin. Dyn. Syst. 29 1001
[11] Mo J Q 2009 Chin. Phys. Lett. 26 010204
[12] Mo J Q 2009 Science in China Ser. G 39 568
[13] Mo J Q, Lin Y H, Lin W T 2010 Acta Phys. Sin. 59 6701 (in Chinese) [莫嘉琪, 林一骅, 林万涛 2010 59 6701]
[14] Mo J Q 2011 Acta Phys. Sin. 60 090203 (in Chinese) [莫嘉琪 2011 60 090203]
[15] Mo J Q 2011 Acta Phys. Sin. 60 020202 (in Chinese) [莫嘉琪 2011 60 020202]
[16] Mo J Q 2010 Commun. Theor. Phys. 53 440
[17] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[18] Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys B 20 070205
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[1] Hu Y Q 2002 Introductory to Atmospheric Thermodynamics and Dynamics —Linear and Nonlinear Thermodynamics of the Atmospheric Non-equilibrium State (Being: Geology Publication) (in Chinese) [胡隐樵 2002 大气热力动力学导论——大气非平衡态线性和非线性热力学 (北京:地质出版社)]
[2] De Groot S K, Mazur P 1962 Non-equillbeium Thermodynamics (Amsterdam: North-Holland Pub. Co.)
[3] Prigogine I 1967 Introduction to Thermodynamics of Irreversible Processes (New York: Interscience Pub.)
[4] Shutts G J 1981 Quart. J. R. Met. So. 107 503
[5] Mhrt L 1986 J. Atmos. Sci. 43 1036
[6] de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation (Amsterdam: North- Holland Publishing Co.)
[7] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[8] Ramos M 2009 J. Math. Anal. Appl. 352 246
[9] D'Aprile T, Pistoia A 2010 J. Differ. Eqs. 248 556
[10] Faye L, Frenod E, Seck D 2011 Discrete Contin. Dyn. Syst. 29 1001
[11] Mo J Q 2009 Chin. Phys. Lett. 26 010204
[12] Mo J Q 2009 Science in China Ser. G 39 568
[13] Mo J Q, Lin Y H, Lin W T 2010 Acta Phys. Sin. 59 6701 (in Chinese) [莫嘉琪, 林一骅, 林万涛 2010 59 6701]
[14] Mo J Q 2011 Acta Phys. Sin. 60 090203 (in Chinese) [莫嘉琪 2011 60 090203]
[15] Mo J Q 2011 Acta Phys. Sin. 60 020202 (in Chinese) [莫嘉琪 2011 60 020202]
[16] Mo J Q 2010 Commun. Theor. Phys. 53 440
[17] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[18] Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys B 20 070205
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