Dynamical analysis, linear feedback control and synchronization of a generalized Lotka-Volterra system

Elsadany, A. A.; Matouk, A. E.; Abdelwahab, A. G.; Abdallah, Hoda Y.

doi:10.1007/s40435-016-0299-x

Cited by 13 publications

(11 citation statements)

References 53 publications

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“…Then, system (36) has the following characteristic equation that is evaluated at the steady state E 1 : Figure 7(a) shows that the states of Samardzija-Greller model (36) approach the steady state E 1 = 1,11,0 . However, Figures 7(b) and 7(c) show that the states of system (36) are not stabilized to the steady state E 1 = 1,11,0 when α = 1 and α = 1 1, respectively. These results illustrate the role of the parameter α on suppressing chaos in Samardzija-Greller model (8).…”

Section: Chaos Control Of Samardzija-greller Systemmentioning

confidence: 97%

“…Oancea et al utilized this system to achieve the pest control in agricultural systems [35]. In 2018, Elsadany et al proved the existence of generalized Hopf (Bautin) bifurcation in this model [36]. Recently, some works investigating synchronization in the fractionalorder Samardzija-Greller model with order less than one have appeared [37][38].…”

Section: Introductionmentioning

confidence: 99%

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Dynamics, Chaos Control, and Synchronization in a Fractional‐Order Samardzija‐Greller Population System with Order Lying in (0, 2)

et al. 2018

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This paper demonstrates dynamics, chaos control, and synchronization in Samardzija-Greller population model with fractional order between zero and two. The fractional-order case is shown to exhibit rich variety of nonlinear dynamics. Lyapunov exponents are calculated to confirm the existence of wide range of chaotic dynamics in this system. Chaos control in this model is achieved via a novel linear control technique with the fractional order lying in (1, 2). Moreover, a linear feedback control method is used to control the fractional-order model to its steady states when 0<α<2. In addition, the obtained results illustrate the role of fractional parameter on controlling chaos in this model. Furthermore, nonlinear feedback synchronization scheme is also employed to illustrate that the fractional parameter has a stabilizing role on the synchronization process in this system. The analytical results are confirmed by numerical simulations.

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Section: Chaos Control Of Samardzija-greller Systemmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Dynamics, Chaos Control, and Synchronization in a Fractional‐Order Samardzija‐Greller Population System with Order Lying in (0, 2)

et al. 2018

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“…1,2 As a famous population dynamical model, it has been extensively researched from different aspects such as modeling, bifurcation and chaos, stability, control, evolutionary dynamics, and so on. [3][4][5][6][7][8][9][10][11][12][13] Xiao et al presented a retarded functional differential equations for the LV model and gave its mathematical analyses. 3 The fractional calculus and fractional order models have been studied in depth as in He, 14 He, 15 and Khan et al 16 and were widely applied to deal with discontinuous problems.…”

Section: Introductionmentioning

confidence: 99%

“…8 An LV model with discrete and distributed delays was proposed and the stability analysis for the model was obtained by LMI approach. 9 Elsadany et al 11 and Wang et al 12 researched the control and synchronization of the LV systems.…”

Section: Introductionmentioning

confidence: 99%

Robust passivity analysis of Markov‐type Lotka–Volterra model with time‐varying delay and uncertain mode transition rates

Wang

Dong²,

Xie³

et al. 2020

Math Methods in App Sciences

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This paper devotes to the global robust passivity problem for a novel Markovian switching Lotka-Volterra (LV) model with time-varying delay. The Markovian switching with uncertain mode transition rates is first drawn into modeling the predator-prey system and the uncertainty of model parameters is also fully discussed, which can reflect the realistic practical significance. The robust passivity for the uncertain LV model with disturbance input and feedback control is studied by the passivity theories and inequality techniques. Some sufficient criteria are derived by the Lyapunov-Krasovskii functional, and the corresponding controllers are designed to ensure the passivity of the proposed closed-loop uncertain LV model. Finally, a three-specie two-mode LV model is provided to illustrate effectiveness of the proposed theoretical results. KEYWORDS Lotka-Volterra model, Markovian process, passivity analysis, uncertain parameters MSC CLASSIFICATION 34H05; 37L55; 92-10; 93B52; 93D30 Math Meth Appl Sci. 2020;43:6976-6984. wileyonlinelibrary.com/journal/mma

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“…It is well known that chaos has potential application values and great prospect in secure communication and other areas [18][19][20][21][22]. Recently, fractional-order chaotic systems and hyperchaotic systems have been studied in a widespread way and have been payed close attention with the deepening of theoretical research of fractional-order systems [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Fuzzy Synchronization of Fractional-Order Chaotic (Hyperchaotic) Systems with Input Saturation and Unknown Parameters

Liu

Chen

et al. 2017

Complexity

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We investigate the synchronization problem of fractional-order chaotic systems with input saturation and unknown external disturbance by means of adaptive fuzzy control. An adaptive controller, accompanied with fractional adaptation law, is established, fuzzy logic systems are used to approximate the unknown nonlinear functions, and the fractional Lyapunov stability theorem is used to analyze the stability. This control method can realize the synchronization of two fractional-order chaotic or hyperchaotic systems and the synchronization error tends to zero asymptotically. Finally, we show the effectiveness of the proposed method by two simulation examples.

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Dynamical analysis, linear feedback control and synchronization of a generalized Lotka-Volterra system

Cited by 13 publications

References 53 publications

Dynamics, Chaos Control, and Synchronization in a Fractional‐Order Samardzija‐Greller Population System with Order Lying in (0, 2)

Dynamics, Chaos Control, and Synchronization in a Fractional‐Order Samardzija‐Greller Population System with Order Lying in (0, 2)

Robust passivity analysis of Markov‐type Lotka–Volterra model with time‐varying delay and uncertain mode transition rates

Adaptive Fuzzy Synchronization of Fractional-Order Chaotic (Hyperchaotic) Systems with Input Saturation and Unknown Parameters

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