Vol. 13, No. 2 (2024): Regular Issue

In this paper an eco-epidemiological model with fading memory for Holling type II functional response is formulated and analyzed.~The fading memory property is that the predator's present growth rate is dependent on past quantities of prey.~The existence, uniqueness, positivity and boundedness of the solutions of the proposed model are investigated. The local asymptotic stability of obtained equilibrium points are discussed. The analytical condition for Hopf bifurcation around the interior equilibrium point of the proposed system is determined. The proposed model undergoes supercritical Hopf bifurcation. Numerical simulations are performed to clarify the characteristics of the obtained analytical results and understand the effects of fading memory on the dynamics of the proposed model. It is observed that varying the fading memory parameter has a sensitive effect on the model dynamics.

In this research article a modified nonlinear Schrödinger equation describing the dynamics of slowly varying envelope of electromagnetic waves in plasmas is studied. Applying perturbation technique approximate solutions are obtained and plotted numerically. The effects of the physical parameters on the obtained solutions are also examined.

In this paper, the Homotopy Analysis Method (HAM) is implemented to obtain the approximate solutions of a nonlinear system of ordinary differential equations such as the obesity epidemic model. The convergence theorem of HAM for the model as well as the regions of convergence derived from the $g$ curves are demonstrated. In addition, an optimal convergence control parameter has been determined. Numerical simulations of the model are carried out using MATLAB and then compared with the results of the Runge-Kutta (RK) method. The simulation results show that if the adult population follow a healthy lifestyle and physical exercises, it reduces the progression of becoming overweight and obese. The graphs and the tables exhibit the simplicity and the reliability of the method.

The present work addresses simplistic approach of synchronization strategy for a class of nonlinear chaotic systems with reduced order observer in master-slave configuration. To establish synchronization objective, the system state dynamics is decoupled into dynamics of measurable and unmeasurable states to obtain the estimation error dynamics. Lyapunov stability criterion based observer stabilizes the estimation error which implies synchronization. Reduced order observer design scheme utilizes only the measurable states of master system for estimation. Even to tackle case of multiple states nonlinearity, only output states of system is required which makes it simpler and economical for practical controllers applications. Moreover, to avoid dependence of reduced order observer on derivative of output state dynamics, suitable coordinate transformation is proposed. For real-time applicability, synchronization effectiveness is utilized for secure chaotic communication using n-cipher encryption-decryption methodology. The derived scheme of synchronization and secure communication is also validated in presence of external random noise but its scope can be extended to class of nonlinear systems as well. For numerical simulations, detailed results for chaotic Lorenz system belonging to addressed class are presented.

As advancements in applied sciences and technology continue, various dissipative nonlinear systems have emerged. However, the conservative systems have received little attention in previous research. The purpose of this paper is to introduce a novel four-dimensional conservative system with hyperchaotic behavior. This system is derived from the Lorenz-like system through the use of a state feedback control strategy. The resulting system features two saddle-focus hyperbolic equilibria. Various dynamical characteristics are examined theoretically and numerically, including its equilibria, Jacobian matrix, Lyapunov exponents, Lyapunov dimension (Kaplan-Yorke dimension), Multistability, and Complete Synchronization. Additionally, numerical simulation using MATLAB 2021 confirms the theoretical results.

Invariant tori (or ``fixed surfaces": attractors for neighboring periodic orbits in a dissipative dynamical system) have been widely studied but the corresponding generalization for quasi periodic orbits have rarely been discussed. Here we investigate ``higher dimensional fixed surfaces" by analyzing a pair of coupled non identical Van der Pol oscillators and also the Kuznetsov oscillator. We find that the renormalization group based approach introduced by Chen, Goldenfeld and Oono is ideally suited for analyzing the quasi periodic analogues of limit cycles. We also address entrainment issues in a pair of forced and coupled Van der Pol oscillators. Our principle finding there is that if two such independent oscillators one with frequency entrainment and the other without are coupled linearly, then it is possible to produce an entrained state via the coupling.

Predator-prey system, which has been widely employed in recent years, offers a suitable mathematical model for presenting the relationship among prey and predators. We will look at a non-linear differential system in this paper. We created two intra-species predator-prey model, one for prey and another for predator, based on the Lotka-Volterra predator-prey model. The Takagi-Sugeno (T-S) impulsive control model and the fuzzy impulsive control model were used to explore the stability of the Lotka-Volterra predator-prey system. Numerical simulation provides the global stabilities and the fuzzy solution.

The proposed analytical investigation deals with the interactions between prey, predator, and scavenger population in the event of prey harvesting through the use of an updated mathematical model. It includes the usage of the modified Previte and Hoffman tri-trophic food web model along with its issues governing the system of nonlinear differential equations. The prey population is assumed to follow a logistic growth with predation from both the predator and the scavenger population. The intervention of prey harvesting is another inclusion of the concerned study for the purpose of having a complete understanding of the influence of both the predator and scavenger species. The present attempt intends to explore the mechanism of harvesting scenario in a three-dimensional system of interacting species, namely one prey and two specialist predators. At the onset, the proposed model is sought for dimension-free so as to reduce the number of model parameters of the system successfully. The existence of feasible equilibria, together with their topological classification regarding coexistence positive equilibrium points of the system is thoroughly examined.~The stability analysis is carried out for all the feasible equilibria of the system in order to understand the dynamics of the interacting species. The sensitivity analysis of the model system is also performed numerically so as to estimate the harvesting rate culpable for balancing biomass. One may perceive that so long as the harvesting rate is uncontrolled, that is, beyond the threshold value, both the predator and scavenger species become extinct together with the prey population.

In this work, we consider a one-dimensional thermoelastic system of the Timoshenko type which was studied by Ghennam and Djebabla. Replacing their boundary conditions by the Dirichlet-Neumann conditions, we prove that the system decays in a general way independently of the system's coefficients which constitutes an improvement of the above-mentioned work. Finally, we provide some numerical results to validate the theoretical results.

This paper is aimed to study the KP-BBM equation, which was proposed by Abdul Majid Wazwaz [Wazwaz. A.M.: Applied Mathematics and Computation, 169 (2005), 700–712.]. To check its integrability Painlevé test has been performed. Lie Symmetry analysis has been done and point symmetry generators are obtained. The invariants of the Lie algebra are found and the one dimensional optimal system for subalgebras of the obtained Lie algebra is constructed by using the Hu-Li-Chen algorithm. Three similarity reductions and corresponding exact solutions are derived.~Also Homogeneous balance method, $Tanh$ method are used to find exact solutions. Solitary wave like solutions are obtained and plotted for some suitable values of the parameters involved. The effects of the nonlinear coefficient and dispersion coefficient on the obtained solitary waves are discussed.

In this work, the perturbation analytical method is used to analyze the nonlinear free vibration of a functionally graded beam on the Winkler-Pasternak elastic basis exposed to mechanical and thermal loadings. The partial differential equation describing the beam's nonlinear motion is first developed under the assumption of the Euler-Bernoulli theory and with the aid of Von-strain-displacement Karman's relation. The Galerkin technique is then used to change the partial differential equation into a nonlinear ordinary differential equation. The ordinary differential equation is resolved using the analytical perturbation method. The effect of boundary conditions, the elastic foundation coefficients (including linear and nonlinear Winkler foundation moduli and elastic shear modulus foundation), axial force, and temperature on the nonlinear natural frequency of FG beams is studied. Results reveal that the presented analytical solution provides accurate predictions with minimum computational effort, as the first-order solution is enough to obtain results with the desired accuracy.

In this paper, the nonlinear thermomechanical analysis of a stayed-beam made with fractional viscoelastic materials subjected to wind load and platoon motion loads under thermal conditions is investigated. Using Newton's second law of motion, the equation of dynamics is derived and reduced to generalized modal forms by applying the Galerkin methods. In the first vibration mode, the analytical study is conducted via multi-scale methods. Following this analytical procedure, the appearance conditions of various types of bifurcation are obtained using linear analysis; the periodic solutions are obtained using nonlinear analysis; then, the effect of fractional viscoelasticity, thermal variation and load spacing on the dynamics of the structure are explained numerically. It is found that, taking into account thermal loads due to temperature change in the environment, material properties and mechanical loads, many complex phenomena or loss of stability depending on the type of external loads can occurs. Thus, the advantageous effects of viscoelastic fractional derivative material, thermal and load spacing are established and it is also found that, depending on the type of loads, the fractional order changes the effect of thermal loads on the structure.

In theoretical ecology, mathematical models are formulated to understand the interaction among species in an ecosystem. This paper explores the dynamics of three predator-prey models with delay in prey-specific growth rate, predator response function, and predator interaction time respectively. Subsequently, the impact of harvesting is analyzed in all the models. It is observed that varying delay could instigate instability in the system via Hopf-bifurcation. Taking harvesting as control can destroy such oscillatory behavior and bring the system to a stable dynamic. In this interplay between these two parameters, stability switching is observed, and such results could not be ascertained in the latter models. We have also inspected the system's behavior at maximum sustainable yield (MSY). If delay is small, harvesting at MSY could produce stable stock. Various numerical simulations are carried out to visualize our analytical findings.

This article concentrates in analysing a stochastic neutral integro-differential equations with infinite delay, fractional Brownian motion and Poisson jumps in concrete-fading memory phase space $\mathcal{C}_{\mu}$. We introduce sufficient conditions to acquire existence and uniqueness of mild solution in the $p$th moment by using stochastic analysis technique, successive approximation method and Grimmer's resolvent operator theory. Moreover, in the later part mean square exponential stability and almost surely exponential stability of solutions are investigated. Finally, an example is provided to validate the obtained results.

The present article investigates peristaltic transport of two immiscible fluids in a channel with the influence of slip and temperature jump conditions at boundary walls. The peristaltic pumping of a non-Newtonian fluid occupies in core region and Newtonian fluid in peripheral region. The exact solutions for flow quantities such as pressure rise, stream function and temperature field in both regions are obtained. The effects of different pertinent parameters on variation of pressure rise along the mean flow rate and temperature distribution are analyzed through graphs. The variations in the interface due to the change in physical parameters are also analyzed. It is noticed that the slip parameters have significant effect on pressure rise and temperature distribution. It is noticed that the temperature profile decreases with increasing first slip parameter and also observed that the temperature profiles increases with increasing values of second slip parameter.