Abstract
In this article, two recent computational schemes [the modified Khater method and the generalized exp−φ(I)–expansion method] are applied to the nonlinear predator–prey system for constructing novel explicit solutions that describe a prototype of an excitable system. Many distinct types of solutions are obtained such as hyperbolic, parabolic, and rational. Moreover, the Hamiltonian system’s characteristics are employed to check the stability of the obtained solutions to show their ability to be applied in various applications. 2D, 3D, and contour plots are sketched to illustrate more physical and dynamical properties of the obtained solutions. Comparing our obtained solutions and that obtained in previous published research papers shows the novelty of our paper. The performance of the two used analytical schemes explains their effectiveness, powerfulness, practicality, and usefulness. In addition, their ability in employing various forms of nonlinear evolution equations is also shown.
Highlights
INTRODUCTIONThe bio-mathematics field has been attracting the attention of many researchers who study many distinct biological models from a mathematical point of view. Examples of such biological models are transmission of impulses, the nervous system, the bacteria cell and its distribution, viruses, DNA, and so on. These fundamental models have been mathematically formulated based on the experimental and statistical data that have been considered as functions and arbitrary constants for construction of these phenomena in isolation by using modern experimental biology. Solving these mathematical models gives a clear representation of the formulated functions and parameters to control these bio-mathematical models
This paper studies a biological model to explain a prototype of an excitable system
● The modified Khater (MK) method’s solutions are more than those obtained by the generalized exp(−φ(I))–expansion (GEE) method
Summary
The bio-mathematics field has been attracting the attention of many researchers who study many distinct biological models from a mathematical point of view. Examples of such biological models are transmission of impulses, the nervous system, the bacteria cell and its distribution, viruses, DNA, and so on. These fundamental models have been mathematically formulated based on the experimental and statistical data that have been considered as functions and arbitrary constants for construction of these phenomena in isolation by using modern experimental biology. Solving these mathematical models gives a clear representation of the formulated functions and parameters to control these bio-mathematical models.. The bio-mathematics field has been attracting the attention of many researchers who study many distinct biological models from a mathematical point of view.1–3 Examples of such biological models are transmission of impulses, the nervous system, the bacteria cell and its distribution, viruses, DNA, and so on.. Examples of such biological models are transmission of impulses, the nervous system, the bacteria cell and its distribution, viruses, DNA, and so on.4,5 These fundamental models have been mathematically formulated based on the experimental and statistical data that have been considered as functions and arbitrary constants for construction of these phenomena in isolation by using modern experimental biology.. The above-mentioned bio-mathematical models have been the focus of many mathematicians and physicists to derive various and more accurate computational, semi–analytical, and numerical schemes.9,10 These schemes aim to construct various explicit traveling wave and solitary wave solutions..
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