In this manuscript, we propose the notion of a strong extended s-suprametric space, a novel extension that outperforms both s-suprametric and extended suprametric spaces. It looks into the aspects of open and closed ball topologies within this structure. It also investigates the concepts of existence and uniqueness using basic contractions viz. Banach and Kannan contractions. Illustrative examples demonstrate how the strong extended s-suprametric space outperforms its extended equivalent. Our examples demonstrate the presence and distinctness of fixed points in this scenario. Furthermore, exploiting these newly launched results, the manuscript investigates the analysis of a boundary value problem, including diffusing chemical material constrained between parallel walls with related concentrations at the boundaries, taking into account supplied raw density and recognized absorbing coefficients. It also applies these insights to a nonlinear boundary value issue involving satellite web coupling in which a thin sheet joins two cylindrical spacecraft. This coupling causes nonlinearity, resulting in a separate boundary value issue influenced by radiation effects within the satellites.

This paper investigates the complex dynamics of a discrete‐time predator–prey system incorporating proportionate prey harvesting. The model is derived from a continuous system using the forward Euler discretization method and extends a previously studied model by introducing a harvesting term. First, the positivity of solutions is established to ensure biological feasibility of the discretized system. We analyze the existence and local stability of biologically feasible fixed points, with particular focus on the interior fixed point. Through rigorous bifurcation analysis, we identify both Neimark–Sacker and period‐doubling bifurcations, revealing transitions from stable equilibria to periodic and chaotic behavior. To manage these complex dynamics, we apply feedback control and hybrid control strategies, both of which are shown to effectively suppress bifurcation‐induced chaos and stabilize the system. Numerical simulations are provided to validate the theoretical results and illustrate rich dynamical behavior, including quasi‐periodic oscillations and strange attractors. Moreover, Codimension 2 bifurcations are identified, including 1:2, 1:3, and 1:4 resonance bifurcations that provide a clear explanation of the transition routes to complex dynamics in the model. The findings emphasize that a moderate level of harvesting can promote coexistence and stability of both prey and predator populations, whereas excessive harvesting may destabilize or collapse the system.

Based on generalized bio-thermoelasticity with mass diffusion model, this paper examines the bio-thermal-diffusion interactions problem in living tissues. A decaying exponentially pulsed heat boundary flux is applied to the surface. The basic equations of generalized bio-thermoelastic-diffusions are considered without energy dissipation and are then expressed in the Laplace domain. Using the eigenvalue approach, the analytical solution in the transformed domain was derived. The results are presented numerically and are shown graphically for, temperature, concentration, stress, displacement, and chemical potential. The blood perfusion rates and the impact of various thermoelastic models on physical quantities are discussed and analyzed using visual graphs. The biomedical responses impacted by the bio-thermo-diffusion model on the wave propagation in biological tissues provide insight into the study of the model.

Mathematical modeling of commensalism provides insights into ecological interactions in which one species benefits while the other remains unaffected. In this study, a discrete-time commensalism model is proposed by incorporating a saturating interaction benefit and an interaction efficiency parameter. In contrast to related models, the proposed formulation accounts for both the saturation of the commensal benefit and the fraction of the host population that is either ineffective or unavailable for interaction. The existence and stability of fixed points are analyzed, and conditions for period-doubling bifurcation are derived using the center manifold and normal form theories. Numerical simulations, including bifurcation diagrams, maximum Lyapunov exponents, phase portraits, and basins of attraction, confirm the theoretical results and reveal periodic, chaotic, and multistable dynamics. The findings demonstrate the important role of interaction efficiency and saturation in shaping commensal dynamics.

This work aims to study the dynamic behavior of a discrete-time chemostat model involving the effect of nutrient recycling, which is a common biological phenomenon usually left out in conventional models. Based on a continuous time model involving the interrelationship between bacterial population and nutrient concentration, a new system with nutrient recycling term is obtained by introducing the process of nutrient recycling from biomass. This model is subsequently transformed to a discrete form using the forward Euler approximation scheme. Existence and stability of all possible equilibria are examined using the characteristic equation. Necessary conditions for stability and bifurcations, including transcritical and flip types, have been derived. It turns out that the considered model cannot experience Neimark–Sacker bifurcation. The results indicate that the recycling parameter plays an important role in changing stability regions and can generate complex dynamics, including oscillations and chaos. Numerical simulations are used to verify the analytical results and to show transitions between different types of system behavior. The results imply that the relationship between nutrient input, bacterial proliferation, and the recycling process has an essential influence on the dynamics and improves the comprehension of discrete ecological models.