Two effective computational schemes for a prototype of an excitable system

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.

[1]  Mostafa M. A. Khater,et al.  Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation , 2017 .

[2]  M. Khater.  Exact traveling wave solutions for the generalized Hirota-Satsuma couple KdV system using the exp(−φ(ξ))-expansion method , 2016 .

[3]  M. Kaplan,et al.  Exponential rational function method for space–time fractional differential equations , 2016 .

[4]  C. You,et al.  Thickness dependence of the interfacial Dzyaloshinskii–Moriya interaction in inversion symmetry broken systems , 2015, Nature Communications.

[5]  M. Khater,et al.  Extended Jacobian Elliptic Function Expansion Method and Its Applications in Biology , 2015 .

[6]  Hongjun Cao,et al.  Stability and bifurcation analysis in a predator–prey system with Michaelis–Menten type predator harvesting , 2017 .

[7]  Zhong Lin Wang,et al.  Networks of triboelectric nanogenerators for harvesting water wave energy: a potential approach toward blue energy. , 2015, ACS nano.

[8]  Francesco Paesani,et al.  Dissecting the Molecular Structure of the Air/Water Interface from Quantum Simulations of the Sum-Frequency Generation Spectrum. , 2016, Journal of the American Chemical Society.

[9]  Peter Stoffer,et al.  Dispersion relation for hadronic light-by-light scattering: theoretical foundations , 2015, 1506.01386.

[10]  Harun-Or Roshid,et al.  Exact traveling wave solutions to the (3+1)-dimensional mKdV–ZK and the (2+1)-dimensional Burgers equations via exp(−Φ(η))-expansion method , 2015 .

[11]  Dianchen Lu,et al.  Numerical solutions of nonlinear fractional Wu–Zhang system for water surface versus three approximate schemes , 2019, Journal of Ocean Engineering and Science.

[12]  F. Belgacem,et al.  Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation , 2016 .

[13]  Mostafa M. A. Khater,et al.  New exact traveling wave solutions of biological population model via the extended rational sinh-cosh method and the modified Khater method , 2019, Modern Physics Letters B.

[14]  Spencer J. Sherwin,et al.  Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods , 2015, J. Comput. Phys..

[15]  Renato Zenobi,et al.  Synthesis of a Two-Dimensional Covalent Organic Monolayer through Dynamic Imine Chemistry at the Air/Water Interface. , 2016, Angewandte Chemie.

[16]  M. Belić,et al.  Oblique resonant optical solitons with Kerr and parabolic law nonlinearities and fractional temporal evolution by generalized exp(−Φ(ξ))-expansion , 2019, Optik.

[17]  C. Bannwarth,et al.  Dispersion-Corrected Mean-Field Electronic Structure Methods. , 2016, Chemical reviews.

[18]  G. B. Airy,et al.  I. On the Regulator of the Clock-work for effecting uniform Movement of Equatoreals , 1840 .

[19]  Mostafa M. A. Khater,et al.  The exp(-φ(ξ))-Expansion Method and Its Application for Solving Nonlinear Evolution Equations , 2015 .

[20]  Meng Liu,et al.  Stability in distribution of a three-species stochastic cascade predator-prey system with time delays , 2017 .

[21]  Yujun Zheng.  Water wave optimization: A new nature-inspired metaheuristic , 2015, Comput. Oper. Res..

[22]  Guodong Liu,et al.  Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps , 2017, Complex..

[23]  Tonghua Zhang,et al.  Dynamics analysis and numerical simulations of a stochastic non-autonomous predator–prey system with impulsive effects , 2017 .

[24]  P. Schreiner,et al.  London dispersion in molecular chemistry--reconsidering steric effects. , 2015, Angewandte Chemie.

[25]  Mostafa M. A. Khater,et al.  Explicit Lump Solitary Wave of Certain Interesting (3+1)-Dimensional Waves in Physics via Some Recent Traveling Wave Methods , 2019, Entropy.

[26]  J. Aars,et al.  An Arctic predator–prey system in flux: climate change impacts on coastal space use by polar bears and ringed seals , 2017, The Journal of animal ecology.

[27]  Mostafa M. A. Khater,et al.  Lump soliton wave solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky equation and KdV equation , 2019, Modern Physics Letters B.

[28]  Mostafa M. A. Khater,et al.  Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method , 2019, AIP Advances.

[29]  Daniel J Murray,et al.  Large area synthesis of a nanoporous two-dimensional polymer at the air/water interface. , 2015, Journal of the American Chemical Society.