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Abstract: Crop and weed plants often compete for water, sunlight, soil moisture, nutrients, etc. However, both of them are capable of offering floral resources to pollinators. Hence, crops, weeds, and pollinators are crucial agro-ecosystem components. Considering this aspect, a nonlinear differential equation model is developed to portray the complex interactions among the variables, viz. crop, weed, and pollinator. The proposed model is mutualism-competitive type, which comprises the mutualism of pollinators with crops and weeds and inter-specific competition between crops and weeds. The purpose of the model is to clarify how interactive dynamics affect the individual populations as time progresses. Therefore, the developed model is examined for qualitative features, including different states of equilibrium, their existences and stabilities, to get an idea of the system’s behaviour in the long run and possible bifurcations that could occur in the system’s dynamics with variation in model parameters. These perceptive qualitative findings are corroborated by numerical simulations demonstrating various dynamical patterns that could appear in the system. Results from the model indicate that coexisting weeds, crops, and pollinators can result in a stable state. Nevertheless, in some circumstances, the system may also exhibit periodic oscillations due to Hopf-bifurcation whenever there is an imbalance in the mutualism between pollinators and crops or the competition between crops and weeds. PubDate: 2025-05-21
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Abstract: Recent research shows that predators not only kill their prey directly, but they also make them fearful, which reduces the rate at which prey species procreate. We present a three-dimensional model of prey-predator with fear in prey along with diseases that affect predators as well as time lag brought on by the population of predators gestating. The boundedness and positive invariance of the suggested system’s solutions have been clarified. We evaluate the equilibrium points and the existence of equilibria have been explained. Additionally, the local stability of each potential equilibrium points is investigated. Fear can stabilise the predator–prey system, according to our mathematical calculations. The system’s Hopf bifurcation has been studied in relation to a number of factors. Moreover, Hopf bifurcation is used to show that time delay has periodic solutions and that time delay is crucial for controlling the system dynamics. To further illustrate the influence that fear may have on the delayed prey-predator model, we looked at connection between fear effects and other characteristics using numerical simulations. To determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solution, explicit formulations based on the normal form theory and the center manifold theorem are provided. The outcome of the theoretical investigation is ultimately validated through numerical simulation. PubDate: 2025-05-06
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Abstract: In this paper, based on tumor-host system including interactions between tumor cells, healthy tissue cells and effector immune cells, we propose a stochastic partial differential equation model to characterize wave pattern formation in tumor growth under the influence of random space-time fluctuations. Further, we perform numerical simulations in order to assess the traveling wave behavior of the solution. For this, we use two different computational methods. PubDate: 2025-05-05
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Abstract: Our context is Filippov systems defined on two-dimensional manifolds having a finite number of tangency points. We prove that topological transitivity is a necessary and sufficient condition for the occurrence of non-deterministic chaos when the Filippov system has non-empty sliding or escaping regions. A fundamental result for continuous flows is the equivalence of topological transitivity and existence of a dense orbit. We prove in our setting that topological transitivity for Filippov systems is indeed equivalent to the existence of a dense Filippov orbit, although, in contrast to the continuous case, we are not able to guarantee that the dense orbit implies the existence of a residual set of dense orbits. Finally, we prove that, in this context, topological transitivity implies strictly positive topological entropy for the Filippov system. This calculation is made using techniques similar to those from symbolic dynamics. PubDate: 2025-04-26
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Abstract: In this paper, we consider the following p-Laplacian problem with Hardy potential: $$\begin{aligned} \begin{aligned} -\text {div}(a(y) \nabla v ^{p-2} \nabla v) + b(y) v ^{p-2} v + \mu \frac{v^s}{ y ^p}&= f(y,v) \ \text {in} \ \Omega ,\\ v&> 0 \ \text {in} \ \Omega , \\ v&= 0 \ \text {on} \ \partial \Omega , \end{aligned} \end{aligned}$$ - div ( a ( y ) ∇ v p - 2 ∇ v ) + b ( y ) v p - 2 v + μ v s y p = f ( y , v ) in Ω , v > 0 in Ω , v = 0 on ∂ Ω , here $$p \in (1,n), \ \Omega \ (\subset {\mathbb {R}}^n)$$ is an exterior domain. We assume that the function f has either superlinear or sublinear growth with respect to the variable v. By using critical point theory, we establish the existence of a weak solution to this problem. PubDate: 2025-04-25
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Abstract: In seismic imaging, understanding the relationship between wavefront-propagation velocity and time-interval velocity is crucial for achieving optimal resolution. However, this task becomes even more challenging when considering anisotropic situations. Over the past century, numerous seismic processing techniques have been developed and applied for practical purposes. However, the majority of these methods are specifically tailored for use in heterogeneous and isotropic models. The advancement of seismic technologies capable of effectively addressing media with anisotropic properties remains a significant technological challenge. To accurately account for the influence of anisotropy on wavefronts, it is essential to have a solid grasp of the underlying physics. Unfortunately, the anisotropy model that best describes the medium is often unknown. To address this issue, we utilize paraxial-ray theory in a ray-centered coordinate system to study the wavefront phenomenon. This approach allows us to develop explicit expressions that describe the physics of the problem. Using this theoretical framework, we can accurately generalize the relationship between time-migration rays and Dix velocity by incorporating the velocity-spreading factor for general anisotropic media. Moreover, the velocity-spreading factor provides valuable information for various applications, including model building, time-imaging, and time-to-depth conversion. In summary, the results presented here provide new tools to develop advanced seismic imaging technologies, which are fundamental to the oil and gas industry. PubDate: 2025-04-25
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Abstract: In this article, we investigate the existence and uniqueness of a positive solution for a class of singular nonlinear elliptic problem with boundary condition. Our result holds in fractional Orlicz-Sobolev spaces. PubDate: 2025-04-23
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Abstract: This research focuses on establishing the existence of second-order solutions for neutral functional differential inclusions. Both finite and state-dependent delays are considered. We employ M$$\ddot{o}$$nch’s fixed point theorem to establish the existence of these solutions, while also utilizing the concept of measures of noncompactness. An example is provided which illustrates our results. PubDate: 2025-04-22
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Abstract: We consider a two-dimensional Burgers system. This system can be written in a potential form. We apply Lie symmetry methods on the system and on its potential form to construct several exact solutions. Also a non-Lie ansatz is used to derive exact solutions. PubDate: 2025-04-21
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Abstract: The coupled mKdV–Calogero–Bogoyavlenskii–Schiff equations are utilized to examine nonlinear wave interactions in fluids, particularly demonstrating nonlinearity at equilibrium attributed to cubic nonlinearity. This research article offers analytical solutions derived from optimal subalgebra classification and classical Lie symmetry analysis. The profiles of positons and negatons were examined utilizing the prominently visible animation framework. Comparisons of the acquired results with prior findings demonstrate the originality of the outcomes. We employ Noether’s theorem to determine the conserved vectors of the system. The solutions may demonstrate their applicability in identifying invariant solutions to nonlinear partial differential equations and in comparing numerical outcomes. PubDate: 2025-04-11
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Abstract: In this study, we investigate the dynamics of a spatial and non spatial prey-predator interaction model that includes the following: (i) fear effect incorporated in prey birth rate; (ii) group defense of prey against predators; and (iii) prey refuge. We provide comprehensive mathematical analysis of extinction and persistence scenarios for both prey and predator species. We investigate how the prey and predator equilibrium densities are influenced by the prey birth rate and fear level. To better explore the dynamics of the system, a thorough investigation of bifurcation analysis has been performed using fear level, prey birth rate, and prey’s death rate caused by intra-prey competition as bifurcation parameter. All potential occurrences of bi-stability dynamics have also been investigated for some relevant sets of parametric values. Our numerical evaluations show that high levels of fear can stabilize the prey-predator system by ruling out the possibility of periodic solutions. Also, our model’s Hopf bifurcation is subcritical in contrast to traditional prey-predator models, which ignore the cost of fear and have supercritical Hopf bifurcations in general. In contrast to the general trend, predator species go extinct at higher values of prey birth rates. We have also found that, contrary to the typical tendency for prey species to go extinct, both prey and predator populations may coexist in the system as intra-prey competition level grows noticeably. We have also been obtained that both prey and predator equilibrium densities increase (decrease) as the prey birth rate (fear level in prey) increases. The stability and Turing instability of associated spatial model have also been investigated analytically. We also perform the numerical simulation to observe the effect of different parameters on the density distribution of species. Different types of spatiotemporal patterns like spot, mixture of spots and stripes have been observed via variation of time evolution, diffusion coefficient of predator population, level of fear factor, and prey refuge. The fear level parameter (k) has a great impact on the spatial dynamics of model system. PubDate: 2025-03-13
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Abstract: The concept of congruence in the sense of affordance formulated by psychologist James J. Gibson between the intrinsic possibilities of objectives and the possibilities resulting from the characteristics and capabilities of the agent gives rise to an intersection problem between the set of states attainable from the agent and the capture basin of the objective. The agent however can only estimate these sets. The application to the co-emergence model of reinforcement in psychology offers to reconsider situations usually seen as resulting from a feedback loop in terms of controlled differential inclusion. It allows for assessing the effect of a treatment to which the patient may respond in a volatile way. The second application to empirical data of anticipated survival over a 15-year horizon shows the mismatch between actual and estimated congruence, with consequences for future consumption planning. A third case concerns time inconsistency in behavioral economics: The capture basin of the target reflecting an agent’s preference for a good at a given date over this increased good at a later date determines all the initial growth rates of the discount factor for which such a preference holds true. Congruence of a given initial growth rate with the target allows for identifying all trajectories that resolve time inconsistency from this growth rate. The formulation of congruence in terms of differential inclusions between agent and objective therefore makes it possible to develop on the original formulation of affordance in a context of non-normative behaviors. PubDate: 2025-03-03
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Abstract: In this study, slant helices are investigated via quasi-frame (abbv. q-frame) in four-dimensional Euclidean space $${\mathbb{E}}^{4}$$. The notion of k-type slant q-helices is introduced in $${\mathbb{E}}^{4}$$. Each of the q-frame fields $$\left\{ {{\mathbf{T}},{\mathbf{N}}_{q} ,{\mathbf{B}}_{q} ,{\mathbf{C}}_{q} } \right\}$$ which makes constant angles with a non-zero fixed axis is surveyed one by one. Also, the conditions for each type of q-helices are obtained and their associations to each other are analyzed in detail. PubDate: 2025-02-24
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Abstract: A new mathematical model to analyze the transmission dynamics of COVID-19, with a focus on the Omicron variant, non-pharmaceutical interventions (NPIs), and environmental contamination, is proposed. We derive the control reproduction number and examine the stability of both disease-free and endemic equilibria. Using the least squares method, the model was calibrated with data from India’s third COVID-19 wave. PRCC and normalized forward sensitivity analysis identified key parameters influencing disease spread, including the transmission rate ($$\beta $$) and the proportion of exposed individuals who become asymptomatically infected ($$\psi $$) as critical factors. The effect of various important parameters on the dynamics is assessed numerically. The proposed model is modified as an optimal control problem. The study concludes that the most effective control strategy is to continuously adjust the five control measures dynamically to minimize the number of infections while keeping costs as low as possible. PubDate: 2025-02-22
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Abstract: This article deals with an efficient numerical method for solving the time fractional Black–Scholes equation governing the European option pricing model and their Greeks. The Caputo fractional derivative involved in time results a mild singularity and forms a layer near the initial time. For discretization, a graded mesh is introduced in the temporal direction, and in space, a uniform mesh is constructed. The L1 scheme is used to discretize the time fractional derivative, while the second-order finite difference approximations are used for the spatial derivatives. The proposed approach effectively resolves the initial layer with a graded mesh in time, achieving higher temporal accuracy of $$\mathcal {O}(N^{-(2-\gamma )})$$. It provides valuable insights into the error bounds through stability and convergence analysis and captures the behavior of option Greeks, highlighting the impact of fractional derivatives. Compared to uniform mesh-based methods and other existing approaches, it demonstrates superior accuracy and efficiency for time-fractional Black–Scholes equations, ensuring space-time higher-order accuracy. Some numerical results on the solution and their Greeks prove the theoretical analysis. The proposed scheme is applied to European option pricing models governed by the time fractional Black–Scholes equation to examine the impact of the fractional derivative on option pricing. PubDate: 2025-02-18
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Abstract: This paper deals with the Neumann boundary controllability of a system of Petrovsky-Petrovsky type which is coupled through the velocities. We are interested in controlling the corresponding state which has two components by exerting only one boundary control force on the system. We prove that, under the usual multiplier geometric control condition and for small coupling coefficient b, there exists a time $$T_b>0$$ such that the system is null controllable at any time $$T> T_b$$. Our approach is based on transposition solutions for coupled systems and both the Hilbert Uniqueness Method (HUM) and the energy multiplier method. PubDate: 2025-02-17
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Abstract: In many nonlinear real-order systems, memory chaos often arises that poses a great difficulty in merging two attractors in large time when two systems start completely different initialized times. We introduce a constructive method that only needs a positive state and, by implementing a nonlinear control law, gives rise to two distinct theorems on synchronization. It is shown that the method has huge potential in synchronizing in memory chaotic systems associated with completely different orders and random initial-time. PubDate: 2025-02-13
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Abstract: This paper presents a one-dimensional Bresse system with thermoelasticity of type III and constant delay. The objective is to investigate and establish the asymptotic behavior of vibrations in a circular arch problem coupled with damping due to the thermal effect subject to constant delay feedback. By applying the semigroup method, we prove that the system is well-posed. Furthermore, with some assumptions on the delay feedback and wave speeds of propagation, we prove that the dissipation through this thermal effect is solely sufficient to counteract the time delay effect and the vibrations in the displacements, thus causing exponential and polynomial energy decay of the system’s solution. Our stability results are achieved by employing the multiplier technique, which mainly involves constructing an appropriate Lyapunov functional equivalent to the system’s energy. PubDate: 2025-02-10
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Abstract: This paper is concerned with the existence and uniqueness of solutions for a semilinear neutral differential equation with impulses and nonlocal conditions. We assume that the nonlinear terms are globally Lipschitz, which allows us to prove the existence and uniqueness of solutions via Banach fixed-point theorem. Finally, we present an example as an application of our method. PubDate: 2025-02-01
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Abstract: In this paper, the dynamics of a three dimensional ODEs system is analized. This differential system corresponds to a Leslie type intraguild predation interaction between three species (a prey population, P; a mesopredator population, MP; and a superpredator population, SP). The main premises to formulate this model are the consideration of fear effects on the prey population induced by MP and SP populations, and that the interactions are governed by general functional responses. In this regard, the main result consists in to show that, independently of the prey growth rate and the functional responses, there are parameter conditions under which the corresponding differential system has a coexistence equilibrium point and it exhibits a Zero Hopf bifurcation, with respect to the parameters $$c_1$$ and $$k_1,$$ which measure the predator coefficient efficiency and the mesopredator fear effect on prey, respectively. On the other hand, on assuming that the prey population has a logistic Richards growth rate and that the functional responses are Holling type, the coexistence of the three species is showed. Finally, derived from the bifurcation results, it is numerically shown that the IGP-model has a chaotic dynamics. This is done by computing the maximum Lyapunov exponents. Moreover, several invariant sets are detected, such as equilibrium points, stable limit cycles, homoclinic orbits and invariant tori. PubDate: 2025-01-10
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