Applied Mathematics and Computation最新文献

In terms of fishery management, if it is not managed carefully, it will lead to the extinction of the species and other unfavorable conditions. In order to strengthen the protection, development and rational utilization of fishery resources, this paper proposes a population capture model with state feedback control based on previous studies, in which the small fish is influenced by the Allee effect, and the catch of the big fish is linearly related with the release of the small fish. Firstly, we give the definition of the Poincaré map of the catch system based on impulsive point series, and study the complex dynamic properties of the map, including single peak, multi-peak functions and multiple jumping points. Moreover, the conditions of existence and the number of jumping points are discussed. At the same time, we analyze its properties including monotonicity, differentiability and fixed point. Secondly, the conditions under which the existence and uniqueness of the order-1 periodic solution are provided, and we address the necessary and sufficient conditions for stability of the order-1 periodic solution. Furthermore, existence of the order-k $(k\ge 2)$ periodic solution is obtained. Finally, correctness of our theoretical results is illustrated by numerical simulations. The results show that under human control, the density of big fish and small fish will maintain periodic benign changes, and fishery resources are sufficient for sustainable development.

There have been numerous studies on collective behavior, among which communication between agents can have a great impact on both the payoff and the cost of making decisions. Research usually focuses on how to improve the collective synchronization rate or accelerate the process of cooperation under given communication cost constraints. In this context, evolutionary game theory (EGT) and reinforcement learning (RL) arise as essential frameworks for tackling this intricate problem. In this study, an adapted Vicsek model is introduced, wherein agents exhibit varying movement patterns contingent on their chosen strategies. Each agent gains a payoff determined by the advantages of collective motion juxtaposed with the cost of communicating with neighboring agents. Individuals choose the objective agents based on the Q-learning strategy and then adapt their strategies following the Fermi rule. The research reveals that the utmost level of cooperation and synchronization can be attained at an optimal communication radius after applying Q-learning. Similar conclusions have been drawn from research on the influence of random noise and relative cost. Different cost functions were considered in the study to demonstrate the robustness of the proposed model and conclusions under a wide range of conditions. (https://github.com/WangchengjieT/VM-EGT-Q)

Traditionally, the evolution of cooperation on structured population assumed the uniform interaction partner between gaming and learning. Yet in real-world society, individuals often act different roles in which environments gaming partners differ from learning partners. This investigation studies the evolution of cooperation under the effects of the diverse selection intensity induced by network asymmetry on two-layer networks, where the gaming and learning environments are modeled by different layers, respectively. It is found that heterogeneous selection intensity can alleviate the cooperation dilemma induced by asymmetry between gaming and learning environments. When selection intensity has a correlation with the edge overlap level of two layers, it is found that both positive correlation and negative correlation can optimize the evolution of cooperation for a moderate overlap level. However, positive correlation performs better than negative correlation in promoting the evolution of cooperation. Moreover, the increasing heterogeneity of selection enhances the evolution of cooperation under positive correlation, yet has different effects on cooperation under negative correlation for different temptations. Furthermore, we prove that the results are robust to the deterministic learning process as well as a higher noise.

Research on reputation-based indirect reciprocity has found profound achievements, elucidating its role in promoting cooperation over selfish actions. However, some evaluation methodologies have limitations, such as the image scoring model, a classic first-order paradigm. Several studies have suggested that higher-order rules with more individual information can enhance the stability of cooperation. In this study, we introduce a reputation incentive mechanism to explore the cooperative differences among various evaluation rules. Specifically, players evaluate their opponents' actions following first-order and second-order evaluation rules, respectively. Given that players possess varying degrees of social influence, the evaluative intensity is influenced by the neighbor environment and updated in each round. This resultant fluctuations in reputation exhibit heterogeneity and dynamism. Numerical simulations based on the spatial prisoner's dilemma game demonstrate that under stringent conditions, the first-order rule can sustain cooperation, while the second-order rule may fail, leading to complete group defection. Under more relaxed conditions, the second-order rule proves more effective in promoting full cooperation than the first-order rule. Our research contributes to understanding the guidance and influence of reputation on collective behavior.

Cellular Automata (CA) is a qualitative simulation method widely used in complex systems. However, the anisotropy of the bottom grid is influenced by the sharp boundary, which leads to the problem of grid-induced anisotropy. It not only makes the CA show the anisotropy in the simulation of isotropic propagation, but also produces errors in the simulation of anisotropic propagation. Through a simple binary CA simulation, this paper discusses reasons and processes of grid anisotropy from three aspects: cellular space, neighbor rules and evolution rules, and the error between CA simulation and standard circle propagation is evaluated. Afterwards, five methods for reducing grid anisotropy are introduced and compared in isotropic and anisotropy propagation simulation. For illustration purpose, these methods are considered in the actual system of isotropic and anisotropic propagation, and then the CA model is successfully applied to the classical isotropic propagation, i.e. the chemical wave in B-Z reaction-diffusion system, and classical anisotropic propagation, i.e. the dendritic growth in crystallization system. The results show that the composition shape of neighboring cells affects the isotropic propagation process of CA simulation, and the square grid is one of potential upgrading methods. The weight of neighbors algorithm is more suitable for simulating diffusion processes, and the limited circular neighbourhood algorithm is more suitable for crystal growth process. These results can be a reference for quantitative application of CA in fields of chemical wave propagation and dendrite growth.

A new approach to overcome the ill-conditioning of the Method of Fundamental Solutions (MFS) combining Singular Value Decomposition (SVD) and an adequate change of basis was introduced in [1] as MFS-SVD. The original formulation considered polar coordinates and harmonic polynomials as basis functions and is restricted to the Laplace equation in 2D. In this work, we start by adapting the approach to the Helmholtz equation in 2D and later extending it to elliptic coordinates. As in the Laplace case, the approach in polar coordinates has very good numerical results both in terms of conditioning and accuracy for domains close to a disk but does not perform so well for other domains, such as an eccentric ellipse. We therefore consider the MFS-SVD approach in elliptic coordinates with Mathieu functions as basis functions for the latter. We illustrate the feasibility of the approach by numerical examples in both cases.

For a graph $G=(V,E)$, the general atom-bond sum-connectivity index is formulated by $AB{S}_{\sigma }\left(G\right)={\sum }_{\xi \zeta \in E\left(G\right)}{\left(\frac{d_{\xi }+d_{\zeta }-2}{d_{\xi }+d_{\zeta }}\right)}^{\sigma }$, where $d_{\xi }$ indicates the degree of vertex $\xi \in V$, σ can be arbitrary real number. Several physicochemical features of benzenoid hydrocarbons can be correctly anticipated using the $AB{S}_{\sigma }$ index. Researchers go through careful inspection of some $AB{S}_{\sigma }$ and reveal that $AB{S}_1$, $AB{S}_{-1}$, $AB{S}_{\frac{1}{2}}$, $AB{S}_3$ enjoy benefit in foreseeing the boiling point, the standard enthalpy of vaporization, the acentric factor, and the entropy of octane isomers, separately. One significant wellspring of information for exploring the molecular construction is the assessed worth of the reach for topological indices through certain predefined molecular graph parameters. The purpose of the present work is to find the highest values of the $AB{S}_{\sigma }$ index for $\sigma \ge 0$ in the set of graphs that were given certain predefined parameters, such as matching number, chromatic number, etc. Furthermore, illustrations of the relevant extremal graphs were provided.

The physical interpretation of a variable-order fractional diffusion equation within the framework of the multiple trapping model is presented. This interpretation enables the development of a numerical Monte Carlo algorithm to solve the associated subdiffusion equation. An important feature of the model is variation in energy density of localized states, when the detailed balance condition between localized and mobile particles is satisfied. The variable order anomalous diffusion equations under consideration can be applied to the description of transient subdiffusion in inhomogeneous materials, the order of which depends on the considered spatial and/or time scale. Examples of numerical solutions for different situations are demonstrated. Considering variable-order fractional drift, we calculate and analyze the transient current curves of the time-of-flight method for samples with varying density of localized states.

In this work, we have studied the evolution of the cooperation and the global synchronization on the Kuramoto model upon random networks with two games, in which one is the evolutionary Kuramoto dilemma and the other is the weak prisoner's dilemma. Agents can gain their payoffs from these two games synchronously. In the evolutionary Kuramoto game, cooperators prefer the formation of local synchronization but pay less cooperative cost. Cooperators in weak prisoner's dilemma can form cooperator clusters because of the network reciprocity. Combining these two games shows a mutual promotion effect upon the order of the global synchronization but a competition effect on the cooperation level. The global synchronization begins to rise only when most agents choose cooperation. It is manifested by the fact that the optimal coupling strength for the highest cooperation level is smaller than that for the highest synchronization level. The high cooperation cost makes defection the most advantageous strategy when the coupling strength reaches rather high, which diminishes the effect of cooperator clusters, and ultimately results in the absence of both cooperators and global synchronization. When agents have more neighbors in the random network, it is observed that cooperation is consistently hindered unless the coupling strength is relatively small. Additionally, there is always an optimal average degree that allows for global synchronization.

Closed-form solutions are derived for some improper integrals used in the Kobayashi Potential (KP) method, using the calculus of residues. These integrals are categorized as waveguiding and radiating, which are single-valued and double-valued, respectively. Both classifications are considered for interior and exterior regions, with respect to the discontinuous boundary. Fourier functional space is used to facilitate contour integration for interior problems. It has been demonstrated that radiating integrals are a limiting case of waveguiding integrals. Therefore, the same strategy can be applied to both types of integrals.