Yazar "Muhammad Waqas Yasin" seçeneğine göre listele

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    Exploring the fixed point theory and numerical modeling of fish harvesting system with Allee effect
    (Springer Science and Business Media LLC, 2025-04-24) Muhammad Waqas Yasin; Mobeen Akhtar; Nauman Ahmed; Ali Akgül; Qasem Al-Mdallal
    Fish harvesting has a major role in nutritive food that is easily accessible for human nourishment. In this article, a reaction-diffusion fish harvesting model with the Allee effect is analyzed. The study of population models is a need of this hour because by using precautionary measures, mankind can handle the issue of food better. The basic mathematical properties are studied such as equilibrium analysis, stability, and consistency of this model. The Implicit finite difference and backward Euler methods are used for the computational results of the underlying model. The linear analysis of both schemes is derived and schemes are unconditionally stable. By using the Taylor series consistency of both schemes is proved. The positivity of the Implicit finite difference scheme is proved by using the induction technique. A test problem has been used for the numerical results. For the various values of the parameters, the simulations are drawn. The dynamical properties of continuous models, like positivity, are absent from the simulations produced by the backward Euler scheme. Implicit finite difference scheme preserves the dynamical properties of the model such as positivity, consistency, and stability. Simulations of the test problem prove the effectiveness of the Implicit finite difference scheme.
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    Mathematical analysis and pattern formation in diffusive predator–prey system
    (Springer Science and Business Media LLC, 2025-01-07) Nauman Ahmed; Muhammad Waqas Yasin; Ali Akgül; Dumitru Baleanu; Ovidiu Tintareanu-Mircea
    Prey-predator interactions are modeled using various dynamical systems and these interactions are affected by several factors. The predation rate of prey, reproduction rate, and prey use various strategies to avoid predation, the movement of the prey and predator species, food, and secured shelter can lead to the emergence of various types of patterns. These patterns in the prey-predator dynamics explain the complicated ecosystem. A reaction-diffusion prey-predator model with harvesting in predator is numerically investigated. A conditionally positivity preserving scheme is used. The von Neumann technique is used for the stability analysis. The Taylor series is used for the consistency analysis and discrete approximation is consistent with the underlying model. Pattern formation is observed for the governing model. The spot, stripe, and spot-stripes patterns are successfully gained that describe the complicated dynamics of the prey-predator dynamics. 3D and 2D simulations are drawn for the underlying model. The underlying model has two equilibria, both are successfully gained. All the theoretical results are verified through the simulations.
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    Reliable numerical scheme for coupled nonlinear Schrödinger equation under the influence of the multiplicative time noise
    (Springer Science and Business Media LLC, 2025-03-28) Muhammad Zafarullah Baber; Nauman Ahmed; Muhammad Waqas Yasin; Muhammad Sajid Iqbal; Ali Akgül; Murad Khan Hassani; Muhammad Jawaz
    In this study, we consider the coupled nonlinear Schrödinger equation under the influence of the multiplicative time noise. The coupled nonlinear Schrödinger equation, which shows the complex envelope amplitudes of the two modulated weakly resonant waves in two polarisations and is used to describe the pulse propagation in high birefringence fibre, has several uses in optical fibres.query:Journal instruction requires a city for affiliations; however, these are missing in affiliation [6]. Please verify if the provided city are correct and amend if necessary. The underlying model is analyzed numerically and analytically as well. For the computational results, the proposed stochastic backward Euler scheme is developed and its consistency is derived in the mean square sense. For the linear stability analysis, Von-Neumann criteria is used, given proposed stochastic scheme is unconditionally stable. The exact optical soliton solutions are constructed with the help of the [Formula: see text]-model expansion technique, which provided us with the Jacobi elliptic function solutions that will explore optical solitons and solitary waves as well. The initial and boundary conditions are constructed for the numerical result by some optical soliton solutions. The 3D, 2D and corresponding contour plot are drawn for the different values of noise. Mainly, the comparison of results is shown graphically in 3D and line plots for some newly constructed solutions by selecting suitable parameters value.
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    Spatio-temporal patterns and Turing–Hopf bifurcation in a spatially extended prey–predator model with ratio-dependent interactions
    (Springer Science and Business Media LLC, 2025-04-16) Muhammad Waqas Yasin; Nauman Ahmed; Ali Akgül; Muhammad Zafarullah Baber; Dumitru Baleanu; Ovidiu Tintareanu-Mircea
    In this manuscript, we investigate the (2+1)-dimensional ratio-dependent prey–predator system. Prey–predator dynamics are a vital component of the eco-system. It provides the basic food for the living organisms. So, we considered the extended prey–predator model. The underlying model has 2 equilibrium points and stability analysis is carried out about the coexistence equilibrium. The condition for the Hopf bifurcation and Turing instabilities are derived. These conditions help to analyze the formation of patterns in the prey–predator system. The dispersion relation shows the changing behavior of Hopf bifurcation and Turing instability from stable to unstable. The bifurcation and Turing instability simulation divide the parametric space into 4 Regions. In Region I, the solution is stable, in Region II there is purely Turing instability, in Region III, there is only Hopf instability and in Region IV there is Hopf as well as Turing instability. Different types of Turing patterns are produced to capture rate parameters. The numerical solution of the model is obtained by positivity preserving finite difference scheme. The applied scheme is von Neumann stable, and consistent with the model. The bounded behavior of a given scheme is established. Mainly, we are focused on the graphical simulations for pattern formation and steady-state analysis. The 3D and 2D visualization for the Turing pattern and numerical solution are drawn for the various parameter values. The numerical simulations endorsed the analytical results.