Vol. 12, No. 3 (2023): Regular Issue

The natural environment of living organisms is not only affected by biotic factors but also by abiotic factors, including omnipresent wind. There has been less exploration on the effects of both biotic and abiotic factors on the dynamics of predator-prey interactions. In this work, we propose and study the dynamics of a predator-prey system incorporating wind effects and prey refuge. A refuge can be described as any strategy to avoid or reduce predation risks. We first prove positivity and boundedness of solutions for the system. We analyze the existence of equilibria under certain parametric restrictions. We also derive sufficient conditions for the global stability of the coexistence equilibrium using a suitable Lyapunov functional. Further dynamical analysis reveals that the system experiences local codimension one bifurcations including Hopf and transcritical bifurcations. Our findings show that when prey refuge is in use, it has a stabilizing effect on the system and also increases the equilibrium density of the prey population while the predator equilibrium density decreases. We also observe that the strength of wind flow has both stabilizing and destabilizing effects. We support our theoretical findings with numerical experiments and give their ecological implications.

Flow in an atherosclerotic vessel is a much-researched topic for over half a century, however very little is known while passing through a realistic vessel. A Mathematical model of blood flow through IVUS-VH (Intravascular ultrasound-virtual histology) derived patient-specific artery under stenotic condition has been developed. The flowing blood in this patient-specific arterial lumen is considered as the Generalised Newtonian fluid. The non-linear coupled governing equations of motion accompanied by appropriate choice of the initial and boundary conditions are solved numerically by MAC (Marker and Cell) method satisfying suitable stability conditions. Simulated results exhibited through their graphical representations predict the dimensionless pressure drop is less for Newtonian model than its non-Newtonian counterpart and the severity of the roughness contributes much to the number and length of the flow separation regions in an atherosclerotic vessel.

This paper is concerned with controlling complex dynamics of a three-dimensional chaotic system consisting of two quadratic cross-products and one square term. We use Pyragas' time-delayed feedback control (TDFC) known as time delay autosynchronization (TDAS) method to stabilize the unstable equilibrium point and unstable periodic orbits of the system. An explicit formula is derived to determine the critical value of time delay $ \tau_{0} $ for which when the delay passes through a certain threshold critical value, the chaotic dynamical system undergoes a Hopf bifurcation. Furthermore, by choosing the appropriate range of feedback strength $ K $ and control parameter $ \tau $ as a free parameters, existence of Hopf bifurcation is investigated theoretically and numerically. Finally, some numerical simulations are presented to verify the analytical results.

In this article, we have studied a mathematical model for one prey and two predator with disease in predator. Here the total population is divided into three classes, namely, prey, sound predator and infected predator. We consider two different nonlinear prey refuge coefficients against the sound predator and infected predator respectively. Also both the sound predator and infected predator are harvested in the proposed dynamical system. The possibility of existence of bionomic equilibrium has been considered. The optimal harvesting policy is studied by using Pontryagin's maximal principle. The optimal harvesting efforts corresponding to the optimal solution have been derived. The positive invariance and boundedness of the solutions of the system are shown. The existence of feasible equilibria and their stability analyses are performed. It is found that the zero equilibrium point is unstable, while other equilibrium points are asymptotically stable under certain conditions. We have investigated that harvesting parameters bear an important role to control the spread of infection. Moreover, the increment of predation rates of sound and infected predator change the stability of prey only equilibrium point to infected predator-free equilibrium point and sound predator-free equilibrium point respectively. Suitable graphical representation with proper discussions are performed in the Numerical simulation section to support the proposed dynamical system.

In this paper, we present a deterministic $SEQIR$ mathematical model that describes the transmission dynamics of COVID-19 that also includes testing procedures in the quarantine stage. The reproduction number $R_0$ is derived with some properties of the model. The stability of equilibrium points is analyzed. An objective function is proposed and optimal control strategies are derived using Pontryagin's Maximum Principle. The existence and uniqueness of an optimality system are demonstrated. Numerical simulations are presented in different scenarios with the control interventions early screening, prevention measures of COVID-19, and following a healthy lifestyle. The main objective of the paper is to eradicate the disease in exposed stage. The chosen control variables helps us to reduce the exposed population.

In this paper, We study a class of delayed SIRS epidemic dynamical models with a general nonlinear incidence rate representing the transfer from susceptible class to infected class. Besides we incorporate a surviving probability from susceptibles to infectious. Throughout the paper, Lyapunov and Euler's stability tools are used to establish the global and local stability for both disease-free and endemic equilibriums depending on reproduction number value $R_0$ and disease-induced death rate. Finally, a sensitivity analysis over basic reproduction number with respect to controllable model's parameters and numerical simulations are presented to illustrate and explain our theoretical results.

In this paper, the stability analysis of T chaotic system has been discussed by two different methods viz., Jacobi stability and linear stability methods. Jacobi stability analysis of T chaotic system has been studied by using geometro-dynamical approach with Kosambi-Cartan-Chern (KCC) theory. The deviation curvature tensor and five KCC invariants are obtained which express the intrinsic properties of nonlinear dynamical system. The dynamical behaviors of deviation vector components near the equilibrium points of T system are also discussed. The phase portrait of deviation vector components reflects the dynamical behavior of T system, which shows the instability and chaotic behaviour near the equilibrium points for a set of parameters.

Boundary value problems have wide applications in science and technology. In this paper, one dimensional heat equation model together with initial and Neumann boundary conditions are presented and we compute the steady state solutions of our concerned problem. Furthermore, we discuss various kinds of Ulam stability analysis for the nonlinear discrete boundary value problem of fractional order $1<\sigma<2$ with Riemann-Liouville fractional difference operator. Finally, some examples are presented to illustrate the main results.

In this paper, we propose the subcell method to couple channel and flood flows. We adopt a 1D Saint Venant channel model with coupling terms and the 2D shallow water flood model. The channel flow is coupled to the flood through the discrete 1D coupling term which we derived in a closed form; while the flood is coupled to the channel flow through the 2D numerical fluxes. Since 1D channel models ignore the evolution of channel lateral discharges which are needed to compute the 2D numerical fluxes at flood/channel interfaces, the problem of recovering channel lateral discharges is a crucial one. To this end, we propose a technique that splits channel cells into two sub-cells and adopt an ad-hoc model based on the y-discharge equation in the 2D shallow water equations. Then, motivated by the hydrostatic reconstruction scheme, the subcell hydrostatic reconstruction scheme is formulated, for the first time, and used to compute the channel lateral discharges. This constitutes the novelty of this work. Also, deriving the 1D discrete coupling term in closed form is another novelty. This approach can be easily implemented without requiring any change to the existing channel or flood solver. We prove that the proposed method is well-balanced and satisfies a no-numerical flooding property, and present some numerical test cases on constant-width channels and rectangular floodplains to demonstrate the accuracy and performance of the method. Our results show that the method computes results with good accuracy, yet performs well. We therefore conclude that including a model for evolving lateral discharges within the channel during a flooding event, leads to a significant improvement in the accuracy of the scheme.

In this work, we have investigated the propagation of solitons in a highly dispersive inhomogeneous medium with Cubic-Quintic-Septic-Nonical nonlinearity terms. Here the exact bright soliton solution is shown with the solitary wave Ansatz solution and expresses the constraint conditions on the physical parameters for the existence of a bright soliton. Furthermore, the expressions for frequency shift and shift of the inverse group velocity of the optical pulse with the coefficients of higher order terms are derived. Also, we have studied experimentally that the simultaneous presence of space-dependent coefficients of higher order nonlinearities at a proper value with dispersions in the solution of the higher order nonlinear Schrödinger equation provides an exact solitary shape that can travel over a long distance without any distortion.

A method has been proposed for reconstructing bifurcation diagrams by estimating the parameter space from only time-series data sets. Here, the time-series data sets are generated from an unknown system with different parameter values and we detect unstable sets in an estimated parameter space for the Hénon map. In this way, chaos in the unknown system can be controlled to stay as an unstable set. With this method, we can identify both the stable and unstable sets even when the parameter values change. Results of numerical experiments are presented for detection of unstable sets of various cycles in the estimated parameter space.

This paper presents a contraction theory based methodology for synchronisation of non-linearly coupled dynamical systems interconnected to constitute a complex network. Here, a systematic control procedure is presented to achieve synchronisation of complex network of proposed strict-feedback like class of nonlinear systems. The non-linear diffusive coupling function between different systems of the network is assumed to be in the form of bidirectional links. The proposed methodology can be applicable to any arbitrarily structure of linear/non-linear, bidirectional or unidirectional N-coupled systems in a network. Rigorous analytical results have been derived for coupled systems interacting through specific nonlinear coupling function which are interconnected in different networked topologies including Ring, Global, Star, Arbitrary etc. The analytical conditions for synchronisation are expressed in terms of bounds on coupling strength which are derived using partial contraction concepts blended with graph theory results. An example of complex networks is simulated to verify the theoretical results.