Bifurcation Properties for Fractional Order Delayed BAM Neural Networks

Xu, Changjin; Liao, Maoxin; Li, Peiluan; Guo, Ying; Liu, Zixin

doi:10.1007/s12559-020-09782-w

Cited by 108 publications

(40 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…e research idea can also be utilized to investigate many other types of fractional-order quaternion-valued neural networks. In addition, we know that Clifford analysis is more general than quaternion one [36,37]. We will study the global uniform stability of Clifford-valued neural networks in the near future.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

New Stability Criterion for Fractional-Order Quaternion-Valued Neural Networks Involving Discrete and Leakage Delays

Tang

2021

Journal of Mathematics

View full text Add to dashboard Cite

In the current work, we are devoted to the issue of uniform stability of fractional-order quaternion-valued neural networks involving discrete and leakage delays. Making use of the contracting mapping theory, we prove that the equilibrium point of the involved fractional-order quaternion-valued neural networks exists and is unique. Taking advantage of mathematical analysis strategy, a sufficient criterion involving delay to verify the global uniform stability for the considered fractional-order quaternion-valued neural networks is set up. Computer simulation figures are displayed to sustain the rationality of the established conclusions. This study generalizes and supplements the research of Xiu et al. (2020).

show abstract

Section: Discussionmentioning

confidence: 99%

“…Du and Lu [27] investigated the finite-time synchronization problem for fractional-order delayed memristor-based neural networks. For more detailed studies, we refer the readers to [28][29][30][31][32][33][34][35][36][37]. However, there are few publications on fractional-order quaternionvalued neural networks.…”

Section: Introductionmentioning

confidence: 99%

New Stability Criterion for Fractional-Order Quaternion-Valued Neural Networks Involving Discrete and Leakage Delays

Tang

2021

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

“…Eshaghi et al [16] investigated the Hopf bifurcation, chaos control and synchronization issue for a chaotic fractional-order model. In details, one can see [17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation dynamics in a fractional-order oregonator model including time delay

Xu¹,

Economics²,

Zhang³

et al. 2021

match

Self Cite

View full text Add to dashboard Cite

Setting up mathematical models to describe the interaction of chemical variables has been a hot issue in chemical and mathematical areas. Nevertheless, many mathematical models are only involved with the integer-order differential equation case. The fruits on fractional-order chemical models are very scarce. In this present work, on the basis of the previous studies, we set up a novel fractional-order delayed Oregonator model. Selecting the time delay as bifurcation parameter, we obtain novel delay-independent bifurcation conditions that guarantee the stability and the appearance of Hopf bifurcation for the fractional-order delayed Oregonator model. The study shows that time delay plays a vital role in controlling the stability and the appearance of Hopf bifurcation of the considered fractional-order delayed Oregonator model. In order to verify the rationality of theoretical results, computer simulations are carried out.

show abstract

“…A lot of researchers think that fractional-order dynamical system can more accurately describe the real phenomenon in realistic world than the classical integer-order ones due to its owned memory trait and hereditary nature [12]. Nowadays a great deal of valuable works on fractional-order dynamical systems have been published (see [13][14][15][16][17][18][19][20][21][22]). In particular, the study on fractional-order predator-prey systems is also continuously displayed.…”

Section: Introductionmentioning

confidence: 99%

Further Results on Bifurcation for a Fractional-Order Predator-Prey System concerning Mixed Time Delays

Yao

Tang

2021

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

In the present work, we mainly focus on a new established fractional-order predator-prey system concerning both types of time delays. Exploiting an advisable change of variable, we set up an isovalent fractional-order predator-prey model concerning a single delay. Taking advantage of the stability criterion and bifurcation theory of fractional-order dynamical system and regarding time delay as bifurcation parameter, we establish a new delay-independent stability and bifurcation criterion for the involved fractional-order predator-prey system. The numerical simulation figures and bifurcation plots successfully support the correctness of the established key conclusions.

show abstract

Bifurcation Properties for Fractional Order Delayed BAM Neural Networks

Cited by 108 publications

References 58 publications

New Stability Criterion for Fractional-Order Quaternion-Valued Neural Networks Involving Discrete and Leakage Delays

New Stability Criterion for Fractional-Order Quaternion-Valued Neural Networks Involving Discrete and Leakage Delays

Bifurcation dynamics in a fractional-order oregonator model including time delay

Further Results on Bifurcation for a Fractional-Order Predator-Prey System concerning Mixed Time Delays

Contact Info

Product

Resources

About