水生生态系统的混沌控制及其分数阶动力学特征任务书

 2021-08-20 12:08

1. 毕业设计(论文)主要目标:

1. 判别一阶水生生态系统超混沌存在性,并用数值模拟的方法进行验证;2. 对混沌系统进行相关控制,使其稳定到系统的平衡点;3. 研究分数阶微分方程局部解的存在性及唯一性。

2. 毕业设计(论文)主要内容:

1.水生生态系统混沌分析;2. 计算Lyapunov指数;3. 一阶微分方程的混沌控制;4. 分数阶微分方程局部解的存在性及唯一性;5. 分数阶系统平衡点的稳定性。

3. 主要参考文献

[1]C. Yang and C. Q. Wu, A robust method on estimation of Lyapunov exponents from a noisy time series, Nonlinear Dynam.64(2011), no.3, 279– 292.[2]F. E. Udwadia and H. F. von Bremen, Computation of Lyapunov characteristic exponents for continuous dynamical systems, Z. Angew. Math. Phys. 53 (2002), no.1, 123– 146.[3]C. Yang, C. Q. Wu and P. Zhang, Estimation of Lyapunov exponents from a time series for n-dimensional state space using nonlinear mapping, Nonlinear Dynam.69(2012), no.4, 1493– 1507.[4]H. Liao, Novel gradient calculation method for the largest Lyapunov exponent of chaotic systems, Nonlinear Dynam. 85(2016), no.3, 1377– 1392. [5]H. Liao, Novel gradient calculation method for the largest Lyapunov exponent of chaotic systems, Nonlinear Dynam. 85 (2016), no.3, 1377– 1392.[6]A. Wolf et al., Determining Lyapunov exponents from a time series, Phys. D 16 (1985), no.3, 285– 317. [7]M. Pakdaman et al., Solving differential equations of fractional order using an optimization technique based on training artificial neural network, Appl. Math. Comput. 293(2017), 81– 95. [8]W. Lin, Global existence theory and chaos control of fractional differential equations, J. Math. Anal. Appl. 332 (2007), no.1, 709– 726.[9]X. Cao et al., Fractional-order model of the disease psoriasis: a control based mathematical approach, J. Syst. Sci. Complex.29(2016), no.6, 1565– 1584. [10]M. Javidi and N. Nyamorady, Numerical behavior of a fractional fifth order dissipative system of magnetoconvection, Appl. Math. Model. 37 (2013), no.14-15, 7653– 7663. [11]F. A. Rihan et al., On fractional SIRC model withSalmonella bacterial infection, Abstr. Appl. Anal.2014, Art. ID 136263, 9 pp. [12]E. Ahmed, A. M. A. El-Sayed and H. A. A. El-Saka, On some Routh-Hurwitz conditions for fractional order differential equations and their applicationsin Lorenz, Rssler, Chua and Chen systems, Phys. Lett. A 358 (2006), no.1, 1– 4. [13]L. K. M. Faina, L. S. Almocera and P. W. Sy, On the bifurcations and multiple endemic states of a single strain HIV model, Acta Math. Appl. Sin. Engl. Ser.30 (2014), no.4, 913– 930. [14]Z. M. Odibat, Adaptive feedback control and synchronization of non-identical chaotic fractional order systems, Nonlinear Dynam. 60(2010), no.4, 479– 487. [15]S. K. Agrawal and S. Das, A modified adaptive control method for synchronization of some fractional chaotic systems with unknown parameters, Nonlinear Dynam. 73 (2013), no.1-2, 907–919. [16]C. Solidoro, G. Pecenik, R. Pastres, D. Franco, C. Dejak, Modelling macroalgae (Ulva rigida) in the Venice lagoon: Model structure identification and firstparameters estimation, Ecol. Model. 94 (1997) 191–206.[17]A. Garulli et al., Integrating identification and qualitative analysis for the dynamic model of a lagoon, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13 (2003), no.2, 357--374. [18]S. R.-J. Jang and J. Baglama, A nutrient-prey-predator model with intratrophic predation, Appl. Math. Comput. 129 (2002), no.2-3, 517–536. [19]S. Jang, J. Baglama, J. Rick, A nutrient–phytoplankton–zooplankton model with a toxin, Math. Comput. Modelling 43 (2006) 105–118.L. J. Alvarez-Vzquez, F. J. FernFernFernndez and R. MuMuMuoz-Sola, Mathematical analysis of a three-dimensional eutrophication model, J. Math. Anal. Appl. 349(2009), no.1, 135–155.[20]W. Ahmad and JC.Sprott, Chaos in fractional-order autonomous nonlinear systems. Chaos Soliton Fract 16(2003),no.2, 339–351.[21]B.Mandelbrot. Some noises with spectrum, a bridge between direct current and white noise. IEEE Trans Inf Theory 13(1967) ,no.2, 289–298.[22]I. Podlubny . Fractional Differentical Equations. Academic Press, San Diego. CA, (1999) p 18.[23]Y. Liu and Y. Xie, Dynamical characteristics of the fractional-order FitzHugh-Nagumo model neuron and its synchronization. Acta Phys Sin 59(2010), no.3, 2147-2155.

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