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";s:4:"text";s:3646:"Figures 4–8 (left) are a waveform of the membrane potential. (9) with (7) are a generalization of HHM [5], and it can be described as follows: The variable p approaches the steady-state value [5]: when the membrane potential V remains constant. The numerical behavior of system (29) and chaotic attractors at α = 1. Also, in this figure, all parts of the action potential are presented including the rapid upraise, downfall, and unexcitable phase, according to the number sequence as follows: Number 1 means that the action potential begins to fire, the sodium channels are now open, and an influx of sodium occurs. By making research easy to access, and puts the academic needs of the researchers before the business interests of publishers. The conductance for each current component can be written in the form [5]: where g¯Naand g¯Kare the maximal conductance of sodium and potassium, respectively, and gL is a constant. Number 5 means that the potassium channels close and the sodium channels begin to leave the refractory phase and reset to its resting phase. Simulating these equations is an important technique in the research, and accordingly, finding effective numerical methods for the DFDEs is a necessary process. A soma is the main body of neuron from which a long cable called an axon is extended. Numerical analysis and mathematical modeling are essential in many areas of modern life. Step by step, the action potential, h, decreases its activities and continues to leave the cell and moves toward the resting value. Our readership spans scientists, professors, researchers, librarians, and students, as well as business professionals. In this chapter, some real-life model problems that can be formulated as ordinary differential equations (ODEs) are introduced and numerically studied. In 2011, Bhalekar and Daftardar-Gejji [25] have been extended the ABM algorithm to solve DDEs of fractional order and presented numerical illustrations to demonstrate utility of the method. 4. introduced the ABM algorithm [29–31] and mean while some error analysis was presented to improve the numerical accuracy. For instance, based on the predictor–corrector scheme, Diethelm et al. In this figure, it observed that the system (29) shows aperiodic chaotic behavior. [41] proposed the fractional-order Chen system with time delay. Contact our London head office or media team here. trailer<] >> startxref 0 %%EOF 20 0 obj <> endobj 31 0 obj<. We are IntechOpen, the world's leading publisher of Open Access books. Cálculo Numérico Computacional: Aplicação na Microeletrônica. And how these are tested and defined? However, there are explicit methods with much better stability properties: Can anyone give me a practical example of nonlinear system equation? Number 2 means that the membrane becomes more positive at this point due to sodium entering the cell. The numerical behavior and chaotic attractors for α(t) = 0.89 – (0.01/100)t and τ = 0.005. method that integrates mathematical theory into solutions for real-world problems, offering the best of both worlds: mathematics and computations. where q = min (δ1+ α (t), δ2), N = [T/h], and C is a positive constant. How? DDEs are differential equations in which the derivatives of some unknown functions at present time are dependent on the values of the functions at previous times. Open Access is an initiative that aims to make scientific research freely available to all. In 1963 [37], he developed a simplified mathematical model for atmospheric convection when he studied the atmospheric convection. 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