Vol. 14, No. 4 (2025): Regular Issue

The aim of this research is to demonstrate that bifurcation, topological properties and critical conditions of nonlinear dynamics can be clearly understood using complete discrimination system for polynomial method (CDSPM). Our conclusion is supported by an example of derivative nonlinear Schrödinger equation (DNLSE) with quintic nonlinearity, which describes how femtosecond pulses travel across nonlinear optical fibre. The results show that CDSPM is not only implemented to achieve the quantitative results such as classification of travelling waves, but also to carry out qualitative analysis of nonlinear differential equations. Jacobian elliptic solutions, hyperbolic function solutions, rational solutions are a few of the optical soliton solutions of DNLSE that are obtained by CDSPM. The qualitative analysis highlights the equilibrium points and the phase portraits of the system. Phase portraits are graphical representations applied in dynamical structures to depict the periodic behavior and the stability of the system. Our findings have broad applications in nonlinear optics, communication physics and other related domains. These chirps either amplify or compress the wave signals in optical fibers and nonlinear electrical transmission lines. The newly discovered chirped soliton solutions of DNLSE are useful in comprehending phenomena when waves are controlled by this kind of equation.

In this article, the interaction dynamics of seals and polar bears have been discussed in the presence of global warming. It is assumed that seals grow logistically in the absence of a polar bear. It is considered that polar bears consume seal through Holling II functional response. It is also assumed that polar bears may grow logistically in the absence of seals and global warming. It is also considered that global warming increases constantly and decreases due to natural decay. Here, most of the model parameters are considered imprecise in nature by taking interval values. Persistence and extinction conditions of seal and polar bears are investigated. The local stability of the model around each equilibrium point is studied. We investigate the model's global stability around the positive equilibrium point. It is observed that the increase in the value of p may decrease the population of the polar bear. It is found that the increase in global warming may reduce the environmental carrying capacity of the polar bear. It is seen that the density of seals, polar bears, and global warming are highly influenced by the uncertain values of the model parameters. It is found that the seal and polar bear may coexist in the environment in the presence of global warming. The conclusions are supported by the presentation of some numerical simulation results.

The dynamics of the predator-prey system with hyperbolic mortality subject to Neumann boundary conditions are investigated. Stability of the positive equilibrium have been discussed through distribution of the eigenvalues. With different initial values, rich spatial patterns in Turing-Hopf domain are obtained. Especially, the labyrinthine-like patterns are also discovered close to the codimension two Turing-Hopf bifurcation point under suitable conditions.

This article considers a fractional analogue of the discrete Keynesian cross model. We propose the corresponding fractional difference equation, which describes the dynamics of national income, and obtain its solution in terms of the discrete Mittag--Leffler function. Further, we discuss the asymptotic behavior of national income described by this solution and offer two numerical examples to show the applicability of established results.

This work examines the analysis of Jacobi stability of the Sprott-C system by using the KCC-theory. The five KCC invariants are obtained to study the system's characteristics. We also calculate the spherical and ellipsoidal ultimate bound of the ecological model. Further, we analyze combination-combination synchronization among chaotic systems with delay and without delay terms. To see the effect of time-delay on combination-combination synchronization we are considering the time-delay ecological chaotic system. By designing suitable controllers, the synchronization among these systems is achieved. Finally, numerical results validate the feasibility of the designed control method.

Thermal convection in partially-ionized plasma is crucial for understanding both astrophysical phenomena and laboratory processes. This study employs both linear and nonlinear analyses to investigate thermal convection within a partially-ionized plasma layer that saturates a porous medium. We use the energy method to analyse stability and apply normal mode analysis to determine instability. The Galerkin method is utilized to solve the resulting eigenvalue problems. The collisional effect significantly influences energy decay, and the principle of exchange of stabilities confirms the absence of oscillatory convection modes. Identical Rayleigh-Darcy numbers from both analyses establish global stability and rule out the possibility of subcritical regions. We find that compressibility and medium permeability delay the onset of thermal convection. Also, rigid-rigid bounding surfaces are found to be more thermally stable compared to free-free surfaces.

The 2022 - 2023 global Mpox outbreak is proclaimed as feasible pandemic by WHO. The present study addresses obscure epidemiological traits of intrahuman Mpox transmission through a deterministic four-dimensional model and its Caputo fractional-order counterpart in the context of memory. Stability conditions around both the infection-free equilibrium and the endemic equilibrium are established. The model is parameterized based on real Mpox data of 2022 - 2023 global outbreak in Nigeria. Numerical simulations are displaying the requirements of non-pharmaceutical and pharmaceutical interventions to control the Mpox transmission. Choosing effectiveness of awareness campaign and recovery rate through antiviral treatment as well as other precautionary measures as Hopf-bifurcation parameters, conditions for subcritical Hopf-bifurcation and supercritical Hopf-bifurcation carried out. Furthermore, the effectiveness of awareness campaign must be increased to upgrade the global Mpox vaccination uptake rate and to curb the potential contact among human beings in order to cut the Mpox transmission chain.

Epilepsy is a common brain disease in the world, and its clinical diagnosis has always been essential in epilepsy treatment. However, the current medical practice mainly relies on the patient's clinical symptoms and the doctor's manual judgment based on electroencephalogram(EEG), which has significant shortcomings in efficiency and accuracy. With the development of machine learning, artificial intelligence is used for the diagnosis of epileptic seizures in practice. In this paper, we established two different input features: only power spectral density (PSD) and recurrence rate (RR) combined with PSD. Such recurrence rate is achieved through the phase state reconstruction of the time-delayed signals. Considering the recursive characteristics, the accuracy for diagnosing epileptic seizures can reach to 99%. We also compared the performance of the two types of input data and discussed the scale of input data on the results. The influence of time-delay parameters in the recurrence rate is studied. The result shows that the diagnosis through power spectral density with recursive rate as dataset is better than that of judging only by power spectral density. By considering the recurrence rate, the intelligent diagnosis accuracy of the neural network improves by varying degrees, ranging from 0.3% to 1.5%, depending on the size of the input data. The specificity of the neural network improves by varying degrees, ranging from 0.2% to 3.4%, depending on the size of the input data. Simultaneously, the sensitivity values also have risen, ranging from 0.1% to 1.7%. With the increase of data scale, the convergence speed of the neural network in earlier iteration stage will be accelerated. In Fig.10 (c) and (d), considering both RR and PSD results in achieving an accuracy of 98% after only 32 iterations, which is comparable to the accuracy achieved after 186 iterations when only considering PSD. In Fig.11 (a) and (b), the curve of 400 PSD with or without RR is the fastest descending curve in their series, which reflects that the convergence speed accelerates as dataset size increases. However, when the data volume gets larger, the CNN network needs more iteration epochs to achieve stable. That's why there is more fluctuation in curve of 400 PSD with or without RR. The research provides a good perspective for clinical diagnosis of epilepsy seizures.

In today's evolving business environment, particularly within the medical sector, companies face significant challenges in boosting sales of Ayurvedic medicines while embracing sustainable practices. This study introduces an innovative approach to managing the unpredictable demand for Ayurvedic medicines and emphasizes the importance of sourcing products sustainably to reduce environmental harm. We propose a cutting-edge inventory model tailored for non-instantaneously deteriorating Ayurvedic medicines, integrating discount policies and bi-level trade credit financing.

In this paper are being studied Turing and Turing--Hopf instabilities of solutions for reaction--diffusion systems under a certain type of nonselfadjoint boundary conditions. The root subspaces of the Laplace operator provided with such boundary conditions form a Riesz basis of subspaces of $L_2(\Omega)$, that allows the standard procedure for the study of spatial or spatiotemporal pattern formation by considering the unstable Fourier normal modes of the linearized perturbations.

In this paper, we consider a nonlinear wave equation with variable exponents and time-varying delay. We prove a global existence result using the well depth method and by a lemma by Komornik, we establish the decay estimates for the solution under suitable assumptions on the variable exponents $m,p$ and the initial data. This work generalizes and extends several works in the literature.

In current study, nonlinear vibration and frequency response analysis of double walled piezoelectric nanoresonator (DWPENR), simultaneously subjected to visco-Pasternak medium, nonlinear van der Waals force and electrostatic excitation is investigated using the Gurtin--Murdoch surface/interface (S/I) and nonlocal theories. For this analysis, Hamilton's principle is used to obtain the governing equations and boundary conditions and Galerkin technique is used to solve the equation of motion. Complex averaging method combined with arc-length continuation is used to achieve the influences of the small-scale, surface effects, elastic medium, van der Waals force, electrostatic and piezoelectric voltages and other parameters on dimensionless natural frequency (DNF), nonlinear frequency response and stability analysis of the DW piezoelectric nanoresonator. It is concluded that ignoring surface and small-scale effects lead to inaccurate results in vibrational response of the DWPENR. It is found that with increasing or decreasing of dimensionless nonlocal parameter and surface/interface parameters, due to increasing or decreasing of DWPENR stiffness, lead to increasing or decreasing DNF, the resonance amplitude and frequency, the range of instability with saddle-node bifurcations and nonlinear softening or hardening behavior and all nonlinear behavior of DWPENR. The obtained results of this study may be useful for designing of nano/micro electro mechanical system and other nano-/micro-smart structures.

In this paper, we study a class of stochastic evolutionary equations driven by colored noise with the time delay in varying phase spaces. We first prove a property of the nonlinear operator $J^\varepsilon_\rho$ and a convergence Lemma. And then, we derive the Lipschitz convergence of center manifolds in varying phase spaces.

This study addresses the global threat of rotavirus, particularly its impact on infants and young children, and emphasizes the importance of integrating rotavirus vaccines into childhood immunization programs, as recommended by the WHO. It highlights the need for promotional efforts to raise awareness, coupled with efficient vaccine inventory management due to perishability, using preservation techniques and cold storage. The study also proposes green technology investments to reduce carbon emissions from vaccine deterioration, aligning with Sustainable Development Goals. Advanced optimization algorithms, such as Ant Colony, Modified Flower Pollination, Cuckoo Search, and Particle Swarm Optimization, are utilized to optimize pricing, preservation, green investments, and replenishment schedules. Numerical experiments demonstrate the effectiveness of these dynamic investment strategies, and sensitivity analysis provides valuable insights for decision-makers. The study concludes by highlighting the role of green technology in managing the social and environmental impacts of vaccine inventories, offering practical solutions and strategic insights for rotavirus disease response.

A new algorithm is described for detecting small changes in the topological structure of the dynamics of a nonlinear system due to perturbations in the driving signals. The proposed approach is based on implementing a covariance-based clustering method on the windowed training dataset of the reconstructed phase space of the dynamical system, and change-point is detected by evaluating the minimum Euclidean distance between all centroids of these clusters and the windowed covariance matrices for the testing data. Applying the proposed approach to the Rössler system, the Hénon-Heiles system and a photoplethysmogram signal when applying small transient perturbations showed its effectiveness at detecting small discontinuities in the dynamics of the system even when the system is chaotic.

This paper proposes an incomplete constraint (IC) method, together with extreme learning machines (ELM) and multilayer perceptrons (MLP), to solve linear partial differential equations (PDEs). Unlike the physics-informed neural networks (PINN) approach, the IC method does not enforce strict adherence to initial and boundary conditions within the neural network architecture, which simplifies formulation and enhances accuracy. Specifically, by employing trial functions generated via ELM/MLP and spatiotemporal sampling-based configuration points, PDEs are discretized into weak optimization problems described as nonlinear algebraic equations. And then, optimal parameters are determined through nonlinear optimization algorithms and iterative. Finally, for a comprehensive error distribution analysis, five numerical examples are provided to verify the validity and efficiency of the proposed method. Numerical results demonstrate it has lower error levels and/or computational costs than PINN and radial basis collocation methods.