Nonlinear Analysis: Modelling and Control
Not a member yet
1157 research outputs found
Sort by
Comparative analysis of classical and stochastic Maccari system of nonlinear equations
Full text linkIn this paper, the exact solutions of classical and stochastic Maccari system is constructed. The exact comparative solutions are examined and plotted. Interesting results in the case of multiplicative noise are formulated and graphically elaborated. The applications of the stochastic Maccari system are added for the physical purpose. The existence of results for the real part of underlying system are discussed first time for a priori estimates. The perturbations, which disturbed the formation of Langmuir waves, are geometrically expressed in this article. Due to the presence of multiplicative noise term, our system brings a real flavor to the dynamics of the problem
Dynamics analysis of a nonlinear controlled predator–prey model with complex Poincaré map
Full text linkIn this paper, we propose a class of predator–prey models with nonlinear state-dependent feedback control in the saturated state. The nonlinear state impulse control leads to a diversity of pulse and phase sets such that the Poincaré map built on the corresponding phase sets behaves like the single-peak function and multi-peak function with multiple discontinuities. We start our study by analyzing the exact pulse and phase sets of models under various cases generated by the dependent parameter space of nonlinear state feedback control, then construct the Poincaré map that is followed by investigating their monotonicity, continuity, concavity, and immobility properties. We also explore the existence, uniqueness, and sufficient conditions for the global stability of the order-1 periodic solutions of the systems. Numerical simulations are carried out to illustrate and reveal the biological significance of our theoretical findings
Stability analysis and stabilization control of discrete-time impulsive switched time-delay systems with all unstable subsystems
Full text linkn this paper, stability analysis and stabilization control of discrete-time impulsive switched time-delay systems with all unstable subsystems are discussed. By utilizing a switching time-varying Lyapunov–Krasovskii functional and the mode-dependent interval dwell-time switching rule, we derive some more general stability theorems for the considered time-delay system with all subsystems being unstable. Moreover, we design a time-varying state feedback controller to ensure the stabilization of the resulting closed-loop system. Eventually, the theoretical findings are demonstrated utilizing numerical examples.
 
Existence of solutions for a fractional Riemann–Stieltjes integral boundary value problem
Full text linkIn this paper, we study a Riemann–Liouville-type fractional Riemann–Stieltjes integral boundary value problem under some conditions regarding the spectral radius of the relevant linear operator. The existence of nontrivial solutions is obtained using topological degree, and our results improve and generalize some results in the literature
A simulation function approach for optimization by approximate solutions with an application to fractional differential equation
Full text linkIn this work, we study the existence and uniqueness of a common best proximity point for a pair of nonself functions that are not necessarily continuous using the simulation function. In the following, we state important common best proximity point theorems as results of the main theorems of this article. This achievement allows us to have an example that covers our main theorem but does not apply to the Banach contraction principle. Finally, an application of a nonlinear fractional differential equation to support the obtained conclusions
Positive solutions for a Hadamard-type fractional p-Laplacian integral boundary value problem
Full text linkIn this paper we study the existence of positive solutions to a Hadamard-type fractional integral boundary value problem using fixed point index. We construct a new linear operator and obtain our main results under some conditions concerning the spectral radius of this linear operator. Our method improves and generalizes some results in the literature
Spatiotemporal dynamics of a diffusive nutrient-phytoplankton model with delayed nutrient recycling
Full text linkIn this paper, we investigate the spatiotemporal dynamics of a diffusive nutrient-phytoplankton model with delayed nutrient recycling. We first study the stability of positive equilibrium and Turing instability induced by diffusion. We then investigate the effect of delay, and it turns out that the value of the rate of recycling k plays an important role in the Hopf bifurcation induced by delay. The delay will and will not induce Hopf bifurcation with low and high level of k, respectively. To reveal the spatiotemporal dynamics, Turing–Hopf bifurcation is carried out, and normal form is derived. Many spatiotemporal dynamics are found, including the coexistence of two stable spatially inhomogeneous periodic solutions or two stable spatially inhomogeneous steadystate solutions
Mixed convection nonaxisymmetric Homann stagnation-point flow under the influence of magnetic field
Full text linkIn the present study, we have investigated the steady mixed convection nonaxisymmetric Homann stagnation-point flow in the presence of a magnetic field over a vertical flat wall immersed in a viscous and incompressible fluid. The magnetic field is applied in the normal direction to the plate. The governing equations are reduced to a system of nonlinear ordinary differential equations with suitable boundary conditions by applying similarity transformations to the equations and the boundary conditions. Using an efficient shooting method, the transformed equations are numerically solved. The solution involves the dimensionless governing parameters: γ representing the shear-to-strain-rate ratio, a mixed convection parameter λ, a magnetic field parameter M, and Prandtl number Pr. An important observation is that dual solutions exist for a certain range of mixed convection parameter λ. It is noticed that critical values λc of λ are found in opposing flow, which produce two solution branches by making saddle-node bifurcation at λ = λc. Numerical results are obtained for representative values of γ, λ, and M and are explored in depth. Through the use of graphs, the properties of the flow and temperature profiles for various values of the governing parameters γ, λ, and M are examined. Also, we examined how the solution varied with λ for representative values of M (magnetic field parameter). A parametric analysis is conducted to investigate how different governing parameters affect the characteristics of fluid flow and temperature. Also, we derive asymptotic results for large λ
A hybrid fixed point theorem for product of two operators in a lattice-ordered Banach algebra with applications to quadratic integral equations
Full text linkWe prove a hybrid fixed point theorem for the product of two operators in a latticeordered Banach algebra and apply to nonlinear hybrid quadratic integral equations of mixed type for proving the existence of maximal and minimal positive integrable solutions under certain mixed conditions of Lipschitzicity and monotonicity of the nonlinear functions. Our main existence result is illustrated with a numerical example as well as with an application to IVPs of nonlinear first-order discontinuous quadratically perturbed ordinary differential equations