[1] |
Huang C X, Huang Y C, Huang L H, et al. Dynamical behaviors of a food-chain model with stage structure and time delays. Adv Differ Equ, 2018, 2018(186):1-26
|
[2] |
Huang C X, Zhang H, Huang L H. Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear density-dependent mortality term. Commun Pure Appl Anal, 2019, 18(6):3337-3349
|
[3] |
Clark C W. Mathematical models in the economics of renewable resources. SIAM Review, 197921(1):81-99
|
[4] |
Du Y, Peng R, Wang M. Effect of a protection zone in the diffusive Leslie predator-prey model. J Differ Equ, 2009, 246(10):3932-3956
|
[5] |
Ji C, Jiang D, Shi N. Analysis of a predator-prey model with modified Leslie-Gower and Holling-type Ⅱ schemes with stochastic perturbation. J Math Anal Appl, 2009, 359(2):482-498
|
[6] |
Ji C, Jiang D, Shi N. A note on a predator-prey model with modified Leslie-Gower and Holling-type Ⅱ schemes with stochastic perturbation. J Math Anal Appl, 2011, 377(1):435-440
|
[7] |
Gupta R P, Chandra P. Bifurcation analysis of modified Leslie-Gower predator-prey model with MichaelisMenten type prey harvesting. J Math Anal Appl, 2013, 398(1):278-295
|
[8] |
Gupta R P, Banerjee M, Chandra P. Bifurcation analysis and control of Leslie-Gower predator-prey model with Michaelis-Menten type prey-harvesting. Differ Equ Dyn Syst, 2012, 20(3):339-366
|
[9] |
Chakraborty K, Das K, Yu H. Modeling and analysis of a modified Leslie-Gower type three species food chain model with an impulsive control strategy. Nonlinear Analysis:Hybrid Systems, 2015, 15:171-184
|
[10] |
Gordon H S. The economic theory of a common property resource:The fishery. J Political Economy, 1954, 62(2):124-142
|
[11] |
Kaczorek T. Reduced-order fractional descriptor observers for a class of fractional descriptor continuoustime nonlinear systems. Int J Appl Math Comput Sci, 2016, 26(2):277-283
|
[12] |
Liu C, Lu N, Zhang Q. Modeling and analysis in a prey-predator system with commercial harvesting and double time delays. Appl Math Comput, 2016, 281:77-101
|
[13] |
Zhang Q, Liu C, Zhang X. Complexity, Analysis and Control of Singular Biological Systems. London:Springer, 2012
|
[14] |
Zhao H, Zhang X, Huang X. Hopf bifurcation and spatial patterns of a delayed biological economic system with diffusion. Appl Math Comput, 2015, 266:462-480
|
[15] |
Zhang Y, Zhang Q, Yan X G. Complex dynamics in a singular Leslie-Gower predator-prey bioeconomic model with time delay and stochastic fluctuations. Physica A:Stat Mech Appl, 2014, 404(24):180-191
|
[16] |
Chakraborty K, Das S, Kar T K. Optimal control of effort of a stage structured prey-predator fishery model with harvesting. Nonlinear Analysis:Real World Applications, 2011, 12(6):3452-3467
|
[17] |
Glöckle W G, Nonnenmacher T F. A fractional calculus approach to self-similar protein dynamics. Biophysical Journal, 1995, 68(1):46-53
|
[18] |
Heymans N, Podlubny I. Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta, 2005, 45(5):765-771
|
[19] |
Hilfer R. Applications of Fractional Calculus in Physics. Singapore:World Scientific, 2000
|
[20] |
Podlubny I. Fractional Differential Equations. San Diego:Mathematics in Science and Engineering, 1999
|
[21] |
Li X W, Liu Z H, Li J, et al. Existence and controllability for nonlinear fractional control systems with damping in Hibert spaces. Acta Math Sci, 2019, 39B(1):229-242
|
[22] |
Hu C Z, Liu B, Xie S F. Monotone iterative solutions for nonlinear boundary value problems of fractional differential equation with deviating arguments. Appl Math Comput, 2013, 222(1):72-81
|
[23] |
Jian H, Liu B, Xie S F. Monotone iterative solutions for nonlinear fractional differential systemswith deviating arguments. Appl Math Comput, 2015, 262(1):1-14
|
[24] |
Wei Z, Li Q, Che J. Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative. J Math Anal Appl, 2010, 367(1):260-272
|
[25] |
Ghaziani R K, Alidousti J, Eshkaftaki A B. Stability and dynamics of a fractional order Leslie-Gower prey-predator model. Appl Math Modell, 2016, 40(3):2075-2086
|
[26] |
Moustafa M, Mohd M H, Ismail A I, et al. Dynamical analysis of a fractional-order Rosenzweig-MacArthur model incorporating a prey refuge. Chaos Solitons and Fractals, 2018, 109:1-13
|
[27] |
Huang C, Cao J, Xiao M, et al. Controlling bifurcation in a delayed fractional predator-prey system with incommensurate orders. Appl Math Comput, 2017, 293:293-310
|
[28] |
Dai L. Singular Control Systems. Berlin:Springer, 1989
|
[29] |
N'Doye I, Darouach M, Zasadzinski M, et al. Robust stabilization of uncertain descriptor fractional-order systems. Automatica, 2013, 49(6):1907-1913
|
[30] |
Nosrati K, Shafiee M. Fractional-order singular logistic map:stability, bifurcation and chaos analysis. Chaos, Solitons and Fractals, 2018, 115:224-238
|
[31] |
Nosrati K, Shafiee M. Kalman filtering for discrete-time linear fractional-order singular systems. IET Control Theory and Applications, 2018, 12(9):1254-1266
|
[32] |
Kaczorek T, Rogowski K. Fractional Linear Systems and Electrical Circuits. Switzerland:Springer, 2015
|
[33] |
Nosrati K, Shafiee M. Dynamic analysis of fractional-order singular Holling type-Ⅱ predator-prey system. Appl Math Comput, 2017, 313:159-179
|
[34] |
Kilbas A, Srivastava H, Trujillo J. Theory and Applications of Fractional Differential Equations. Amsterdam:Elsevier, 2006
|
[35] |
Kai D. The Analysis of Fractional Differential Equations. Berlin:Springer, 2010
|
[36] |
Zhang H, Cao J D, Jiang W. Reachability and controllability of fractional singular dynamical systems with control delay. J Appl Math, 2013, 2013(1):1-10
|
[37] |
Petráš I. Fractional-Order Nonlinear Systems. Beijing:Higher Education Press, 2011
|
[38] |
Zhang X F, Chen Y Q. Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order, α:The 0
|
[39] |
Yang C, Zhang Q, Zhou L. Stability Analysis and Design for Nonlinear Singular Systems. Berlin:Springer, 2013
|
[40] |
Venkatasubramanian V, Schattler H, Zaborszky J. Local bifurcations and feasibility regions in differentialalgebraic systems. IEEE Trans Automatic Control, 1995, 40(12):1992-2013
|
[41] |
Beardmore R E. The singularity-induced bifurcation and its Kronecker normal form. SIAM J Matrix Anal Appl, 2001, 23(1):126-137
|
[42] |
Agrawal O P. A formulation and numerical scheme for fractional optimal control problems. J Vibr Contr, 2008, 14(9/10):1291-1299
|
[43] |
Atanackovic T M, Stankovic B. On a numerical scheme for solving differential equations of fractional order. Mechanics Research Communications, 2008, 35(7):429-438
|