Numerical solutions of nonlinear biochemical model using a hybrid numerical-analytical technique

Edeki, S.O.; Owoloko, E. A.; Osheku, A. S.; Opanuga, A. A.; Okagbue, Hilary I.; Akinlabi, G. O.

doi:10.12988/ijma.2015.412411

Cited by 8 publications

(4 citation statements)

References 14 publications

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“…e parameters α 1 , α 2 , and α 3 are all dimensionless. Edeki et al [4] used a hybrid approach to investigate the numerical solution of the following biochemical system:…”

Section: Review Of Literature and Statement Of The Problemmentioning

confidence: 99%

Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System

2022

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The local dynamics, chaos, and bifurcations of a discrete Brusselator system are investigated. It is shown that a discrete Brusselator system has an interior fixed point P 1 , r if r > 0 . Then, by linear stability theory, local dynamical characteristics are explored at interior fixed point P 1 , r . Furthermore, for the discrete Brusselator system, the existence of periodic points is investigated. The existence of bifurcations around an interior fixed point is also investigated and proved that the discrete Brusselator model undergoes hopf and flip bifurcations if r , h ∈ ℋℬ | P 1 , r = r , h , h = 2 − r and r , h ∈ ℱℬ | P 1 , r = r , h , h = 4 / 2 − r − r 2 − 4 r , respectively. The next feedback control method is utilized to stabilize the chaos that exists in the discrete Brusselator system. Finally, obtained results are verified numerically.

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“…e parameters α 1 , α 2 , and α 3 are all dimensionless. Edeki et al [4] used a hybrid approach to investigate the numerical solution of the following biochemical system:…”

Section: Review Of Literature and Statement Of The Problemmentioning

confidence: 99%

Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System

2022

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“…Over the years, several research studies on fuzzy differential equations have been executed by scholars adopting numerical methods of single-step methods, multistep methods, predictor-corrector system, Leffler kernel differential operator of the ABC approach, reproducing kernel method (RKM), reproducing kernel Hilbert space method (RKHSM), reproducing kernel theory (RKT) The ideas behind numerical technics are due to the exact results of some FDEs been disadvantage and windy to find out on account of the ramification of the FDEs. Various bookmen talked about and employ the Adams family of predictor-corrector pair for resolving FDEs [4], [5], [7], [12], [13], [14], [17], [20], [36] and [39]. Although, all of these methods resolve to predict and correct the result without a desirable step size to decide the convergence to maximize error with error control.…”

Section: Introductionmentioning

confidence: 99%

The Extended Block Predictor-Block Corrector Method for Computing Fuzzy Differential Equations

Oghonyon

Egharevba

Imaga

2022

Wseas Transactions on Mathematics

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Over the years, scholars have developed predictor-corrector method to provide estimates for ordinary differential equations (ODEs). Predictor-corrector methods have been reduced to predicting-correcting method with no concern for finding the convergence-criteria for each loop with no suitable vary step size in order to maximize error. This study aim to consider computing fuzzy differential equations employing the extended block predictor-block corrector method (EBP-BCM). The method of interpolation and collocation combined with multinomial power series as the basis function approximation will used. The principal local truncation errors of the block predictor-block corrector method will be utilized to bring forth the convergence criteria to ensure speedy convergence of each iteration thereby maximizing error(s). Thus, these findings will reveal the ability of this technique to speed up the rate of convergence as a result of variegating the step size and to ensure error control. Some examples will solve to showcase the efficiency and accuracy of this technique.

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“…Mathematical models of chemistry, physics, physiology, psychology, ecology, engineering, and social sciences have given birth to major areas of research during the last few decades. For instance, Edeki et al [1] have explored the numerical solution of the following nonlinear biochemical model by using the hybrid technique:…”

Section: Introductionmentioning

confidence: 99%

Neimark–Sacker Bifurcation of a Two-Dimensional Discrete-Time Chemical Model

Khan

2020

Mathematical Problems in Engineering

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In this paper, the local dynamics and Neimark–Sacker bifurcation of a two-dimensional glycolytic oscillator model in the interior of ℝ+2 are explored. It is investigated that for all α and β, the model has a unique equilibrium point: Pxy+α/β+α2,α. Further about Pxy+α/β+α2,α, local dynamics and the existence of bifurcation are explored. It is investigated about Pxy+α/β+α2,α that the glycolytic oscillator model undergoes no bifurcation except the Neimark–Sacker bifurcation. Some simulations are given to verify the obtained results. Finally, bifurcation diagrams and the corresponding maximum Lyapunov exponent are presented for the glycolytic oscillator model.

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Numerical solutions of nonlinear biochemical model using a hybrid numerical-analytical technique

Cited by 8 publications

References 14 publications

Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System

Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System

The Extended Block Predictor-Block Corrector Method for Computing Fuzzy Differential Equations

Neimark–Sacker Bifurcation of a Two-Dimensional Discrete-Time Chemical Model

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