Modelling hiding behaviour in a predator-prey system by both integer order and fractional order derivatives

Barman, Dipesh; Roy, Jyotirmoy; Alam, Shariful

doi:10.1016/j.ecoinf.2021.101483

Cited by 11 publications

(8 citation statements)

References 62 publications

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“…Proof. To prove this non-negativity condition, we apply reductio ad absurdum (contradiction method), which is also used in Barman et al [24] and Maji [32]. We assume that there exists t > 0 such that…”

Section: Theorem 4 If the Initial Condition In Rmentioning

confidence: 99%

“…After Riemann and Liouville generalized the concept of integer-order calculus to the fractional-order calculus over two decades ago, the studies about the predator-prey models with fractional-order differential equation have gained much attention, for example, Rahmi et al [22], Owolabi [23], Barman et al [24], Ghanbari and Djilali [25], Yousef et al [26], Ghosh et al [27], and Panigoro et al [28]. The fractional-order derivatives are defined as an integration that provides the ability to store the whole memory over time, and hence, it could give an exact description of different ecological phenomena.…”

mentioning

confidence: 99%

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Bifurcation analysis of a predator–prey model involving age structure, intraspecific competition, Michaelis–Menten type harvesting, and memory effect

Panigoro

Rahmi

Resmawan

2023

Front. Appl. Math. Stat.

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The complexity of the dynamical behaviors of interaction between prey and its predator is studied. The prey and predator relationship involves the age structure and intraspecific competition on predators and the nonlinear harvesting of prey following the Michaelis–Menten type term. Some biological validities are shown for the constructed model such as the existence and uniqueness as well as the non-negativity and boundedness of solutions. Three equilibrium points, namely the origin, axial, and interior points, are found including their global dynamics by employing the Lyapunov function along with the generalized Lassale invariant principle. The changes in dynamical behaviors driven by the harvesting and the memory effect are exhibited, including transcritical, saddle-node, backward, and Hopf bifurcations. The appearance of these interesting phenomena is strengthened by giving numerical simulations consisting of bifurcation diagrams, phase portraits, and their time series.

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Section: Theorem 4 If the Initial Condition In Rmentioning

confidence: 99%

mentioning

confidence: 99%

Bifurcation analysis of a predator–prey model involving age structure, intraspecific competition, Michaelis–Menten type harvesting, and memory effect

Panigoro

Rahmi

Resmawan

2023

Front. Appl. Math. Stat.

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“…Huang et al [16] explored the Hopf bifurcation issue of fractional-order neural networks with leakage delays. For more related studies, one can see [1,2,15,24,33,35,38].…”

Section: Geysermans and Nicolismentioning

confidence: 99%

Bifurcation Anti-Control Tactics of a Fractional-Order Stable Chemical Reaction System

Liu¹

2022

MATCH

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Establishing suitable differential dynamical models to describe the real natural phenomenon in chemistry and physics has become a very hot topic in nowadays society. In this present research, we deal with a fractional-order chemical reaction system. Taking advantage of the fixed point theorem, we prove the existence and uniqueness of the fractional-order chemical reaction system. Using the inequality skill, we prove the non-negativeness of the fractional-order chemical reaction system. By applying a suitable function, we prove the uniform boundedness of the solution to the fractional-order chemical reaction system. With the aid of a hybrid controller including state feedback and parameter perturbation, we discuss the Hopf bifurcation anti-control issue of the fractional-order stable chemical reaction system. A novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation of the involved fractional-order stable chemical reaction system is set up. The study manifests that the delay in the hybrid controller plays a vital role in stabilizing the system and controlling the occurrence of Hopf bifurcation of the fractional-order stable chemical reaction system. In order to validate the derived key conclusions, MATLAB simulations are executed and bifurcation plots are given. The obtained results of this article have momentous theoretical guiding value in controlling the chemical compositions. The exploration idea can also be utilized to investigate the bifurcation control and bifurcation anti-control problems in lots of other fractional-order differential systems in numerous disciplines.

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“…For instance, Ci et al [26] dealt with the multiple asymptotical

\omega

‐periodicity for a kind of fractional neural networks owing delays; Du and Lu [27] explored the adaptive finite‐time synchronization issue in a class of fractional fuzzy cellular neural network models involving delays; Rihan and Rajivganthi [28] investigated the Hopf bifurcation and stability of fractional predator–prey system involving Holling‐type III function and delay; Alidousti and Ghafari [29] analyzed the stability and bifurcation phenomenon in a fractional predator–prey system involving group defense. For more concrete aspects, one can see previous studies [30–34].…”

Section: Introductionmentioning

confidence: 99%

Novel extended mixed controller design for bifurcation control of fractional‐order Myc/E2F/miR‐17‐92 network model concerning delay

Peng

et al. 2023

Math Methods in App Sciences

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MiR‐17‐92 has a vital effect on the adjustment of the Myc/E2F protein in chemistry. In this work, we propose a novel fractional‐order delayed Myc/E2F/miR‐17‐92 network model that revels the relation between miR‐17‐92, E2F, and Myc. Taking advantage of Laplace transform, we obtain the characteristic equation of the established fractional‐order delayed Myc/E2F/miR‐17‐92 network model. By virtue of stability theorem and bifurcation criterion of fractional‐order dynamical equation, a novel delay‐independent condition guaranteeing the stability and the generation of bifurcation phenomenon of the involved model is acquired. By exploiting a proper extended mixed controller (including controller and delayed feedback controller), we efficiently control the stability domain and the emergence of bifurcation for the the involved model. By utilizing another suitable extended mixed controller (including controller and hybrid controller), we can successfully adjust the stability domain and the emergence of bifurcation for the the involved model. The research indicates that delay plays a vital role in stabilizing system and controlling bifurcation of the fractional‐order delayed Myc/E2F/miR‐17‐92 network model. Computer experiment results illustrate the scientificity of the gained key analytical outcomes. The acquired results in this research are totally innovative and own immense theoretical meaning in regulating the concentrations of different proteins.

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Modelling hiding behaviour in a predator-prey system by both integer order and fractional order derivatives

Cited by 11 publications

References 62 publications

Bifurcation analysis of a predator–prey model involving age structure, intraspecific competition, Michaelis–Menten type harvesting, and memory effect

Bifurcation analysis of a predator–prey model involving age structure, intraspecific competition, Michaelis–Menten type harvesting, and memory effect

Bifurcation Anti-Control Tactics of a Fractional-Order Stable Chemical Reaction System

Novel extended mixed controller design for bifurcation control of fractional‐order Myc/E2F/miR‐17‐92 network model concerning delay

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