PDϑ Control Strategy for a Fractional‐Order Chaotic Financial Model

Xu, Changjin; Liao, Maoxin; Li, Peiluan; Xiao, Qimei; Yuan, Shuai

doi:10.1155/2019/2989204

Cited by 5 publications

(4 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the past two decades, fractional calculus and its applications have been applied into various fields due to its accurate describing in many scientific fields, such as fractional stochastic noise [1], fraction order memristive chaotic circuits [2], fractional order financial models [3], and fractional order relaxation-oscillation models [4]. Also, it has wide application in various research areas, which one can find in the references [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Difference monotonicity analysis on discrete fractional operators with discrete generalized Mittag-Leffler kernels

2021

View full text Add to dashboard Cite

In this paper, we present the monotonicity analysis for the nabla fractional differences with discrete generalized Mittag-Leffler kernels $( {}^{ABR}_{a-1}{\nabla }^{\delta ,\gamma }y )(\eta )$ ( a − 1 A B R ∇ δ , γ y ) ( η ) of order $0<\delta <0.5$ 0 < δ < 0.5 , $\beta =1$ β = 1 , $0<\gamma \leq 1$ 0 < γ ≤ 1 starting at $a-1$ a − 1 . If $({}^{ABR}_{a-1}{\nabla }^{\delta ,\gamma }y ) ( \eta )\geq 0$ ( a − 1 A B R ∇ δ , γ y ) ( η ) ≥ 0 , then we deduce that $y(\eta )$ y ( η ) is $\delta ^{2}\gamma $ δ 2 γ -increasing. That is, $y(\eta +1)\geq \delta ^{2} \gamma y(\eta )$ y ( η + 1 ) ≥ δ 2 γ y ( η ) for each $\eta \in \mathcal{N}_{a}:=\{a,a+1,\ldots\}$ η ∈ N a : = { a , a + 1 , … } . Conversely, if $y(\eta )$ y ( η ) is increasing with $y(a)\geq 0$ y ( a ) ≥ 0 , then we deduce that $({}^{ABR}_{a-1}{\nabla }^{\delta ,\gamma }y )(\eta ) \geq 0$ ( a − 1 A B R ∇ δ , γ y ) ( η ) ≥ 0 . Furthermore, the monotonicity properties of the Caputo and right fractional differences are concluded to. Finally, we find a fractional difference version of the mean value theorem as an application of our results. One can see that our results cover some existing results in the literature.

show abstract

Section: Introductionmentioning

confidence: 99%

Difference monotonicity analysis on discrete fractional operators with discrete generalized Mittag-Leffler kernels

2021

View full text Add to dashboard Cite

show abstract

“…Furthermore, it is found that fractional-order differential system has the advantages of simple modeling, clear parameter meaning, and accurate description for some materials and processes with memory and genetic characteristics [15][16][17]. Hence, fractional calculus has become a new mathematical tool favored by researchers, and more and more study of practical problems introduces the theory of fractional calculus and remarkable achievements have been made [18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Control of a Delayed Fractional Mosaic Disease Model for Jatropha curcas with Farming Awareness

2020

View full text Add to dashboard Cite

In this paper, the bifurcation control of a fractional-order mosaic virus infection model for Jatropha curcas with farming awareness and an execution delay is investigated. By analyzing the associated characteristic equation, Hopf bifurcation induced by the execution delay is studied for the uncontrolled system. Then, a time-delayed controller is introduced to control the occurrence of Hopf bifurcation. Our study implies that bifurcation dynamics is significantly affected by the change of the fractional order, the feedback gain and the extended feedback delay provided that the other parameters are fixed. A series of numerical simulations is performed, which not only verifies our theoretical results but also reveals some specific features. Numerically, we find that the Hopf bifurcation gradually occurs in advance with the increase of the fractional order, and there exist extreme points for the feedback gain and the extended feedback delay which can minimize the bifurcation value.

show abstract

“…In the past decades, fractional calculus has been applied into various fields because of its accurate describing in many interdisciplinary fields, such as fraction-order memristive chaotic circuit [20], fractional stochastic noise [21], fractional-order relaxation-oscillation model [22], and fractional-order financial model [23]. With the expansion of application fractional calculus, dynamics of fractional-order system have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Fraction-Order Hopfield Neuron Network and Noise-Induced Coherence Resonance

Shi

Wang

2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this paper, dynamical behaviors of fraction-order Hopfield neuron network are investigated. Firstly, Mittag-Leffler stability analysis is carried out and some sufficient conditions are obtained. On the basis of theoretical analysis, two criteria for determining the stability of fraction-order Hopfield neuron network are presented and comparison between them is given by theoretical analysis along with numerical simulation. According to the proposed criteria, by selecting suitable system parameters, it can be obtained that fraction-order Hopfield neuron network can stabilize to the equilibrium point or an attractor, which can be a periodic orbit or two points. Secondly, considering the inevitable noise in the complex environment of neuron network, the effect of noise on the dynamics of fraction-order Hopfield neuron network is discussed via calculating coefficient of variation and numerical simulations. Results suggest that random noise can cause coherence resonance in fraction-order Hopfield neuron network for certain noise intensity.

show abstract

PD^ϑ Control Strategy for a Fractional‐Order Chaotic Financial Model

Cited by 5 publications

References 49 publications

Difference monotonicity analysis on discrete fractional operators with discrete generalized Mittag-Leffler kernels

Difference monotonicity analysis on discrete fractional operators with discrete generalized Mittag-Leffler kernels

Bifurcation Control of a Delayed Fractional Mosaic Disease Model for Jatropha curcas with Farming Awareness

Stability Analysis of Fraction-Order Hopfield Neuron Network and Noise-Induced Coherence Resonance

Contact Info

Product

Resources

About