Mathematical Methods in the Applied Sciences最新文献_第6页

Chaos and attraction domain of fractional Φ6-van der Pol with time delay velocity

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-10-25 DOI: 10.1002/mma.10545

Zhikuan Xie, Jiaquan Xie, Wei Shi, Yuanming Liu, Jialin Si, Jiani Ren

{"title":"Chaos and attraction domain of fractional \u0000Φ6-van der Pol with time delay velocity","authors":"Zhikuan Xie, Jiaquan Xie, Wei Shi, Yuanming Liu, Jialin Si, Jiani Ren","doi":"10.1002/mma.10545","DOIUrl":"https://doi.org/10.1002/mma.10545","url":null,"abstract":"This article investigates the chaotic analysis and attractive domain of a fractional-order \u0000<math>\u0000 <msup>\u0000 <mo>Φ</mo>\u0000 <mn>6</mn>\u0000 </msup></math>-van der Pol with time delay velocity under harmonic excitation. Firstly, eight different types of bifurcation states of the system under different parameters are calculated by using the undisturbed system. Secondly, the Melnikov method is used to explore the effect of time delay velocity on the threshold of chaos in the Smale horseshoe sense under the double-well potential and three-well potential of the system. Finally, through numerical analysis of the phase diagram, bifurcation diagram, and maximum Lyapunov exponent, the influence of time delay velocity on system chaos is studied. The results indicate that an increase in the delay velocity coefficient will lead to the system transitioning from a chaotic state to a periodic state, while an increase in the delay velocity term will lead to the system transitioning from a periodic state to a chaotic state. In the study of system bifurcation, it is found that the position of the equilibrium points of the system changes during periodic motion. Therefore, cell mapping is used to draw the attractive domain of the system is studying the influence of initial conditions on the equilibrium point of the system and the results show that there is a close relationship between the attraction domain and the process of chaos occurrence.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4262-4278"},"PeriodicalIF":2.1,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143381073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stability and qualitative dynamics of a class of three-dimensional difference equation system of exponential type

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-10-25 DOI: 10.1002/mma.10554

Stephen Sadiq, Nayyer Falak Sher, Abdul Khaliq, Muhammad Shabbir

引用次数: 0

Trace regularization problem for a fourth-order differential operator on separable Banach space

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-10-25 DOI: 10.1002/mma.10564

Ozlem Baksi, Yonca Sezer, Seda K. Caliskan

引用次数: 0

Optimal decay of the Boltzmann equation

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-10-25 DOI: 10.1002/mma.10562

Guochun Wu, Wanying Yang

{"title":"Optimal decay of the Boltzmann equation","authors":"Guochun Wu, Wanying Yang","doi":"10.1002/mma.10562","DOIUrl":"https://doi.org/10.1002/mma.10562","url":null,"abstract":"The Boltzmann equation is a typical example of partially dissipative equations, where the linearized collision operator is positive definite with respect to the microscopic part and the dissipation of the hydrodynamic part is discovered from the coupling structure between the transport operator and the linearized collision operator. Guo and Wang (Comm. Partial Differential Equations, 37, 2012) developed a general energy method for proving the optimal time decay rates of the solution to such type of equations in the whole space; however, the decay rate of the highest order spatial derivatives of the solution is not optimal. In this paper, by incorporating the high-low frequency decomposition in the energy estimates, both linearly and nonlinearly, we prove the optimal decay rates of any high order spatial derivatives of the low frequency part of the solution to the Boltzmann equation and the almost exponential decay rate of the high frequency part, which imply in particular the optimal decay rate of the highest order spatial derivatives of the solution. Moreover, the velocity-weighted assumption of the initial data required in Guo and Wang (Comm. Partial Differential Equations, 37, 2012) is removed by capturing the time-weighted dissipation estimates via the time-weighted energy method. The method can be applied to the compressible Navier–Stokes equations and many partially dissipative equations in kinetic theory and fluid dynamics.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4542-4553"},"PeriodicalIF":2.1,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143381072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The uniqueness of minimizers for L2-subcritical inhomogeneous variational problems with a spatially decaying nonlinearity

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-10-25 DOI: 10.1002/mma.10575

Yunxia Fu, Xinji Liu, Shuang Wu

引用次数: 0

Stability of planar diffusion wave for three-dimensional bipolar Euler–Poisson system with time-dependent over-damping

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-10-24 DOI: 10.1002/mma.10560

Qiwei Wu, Xiaofeng Hou

引用次数: 0

Imperfect bifurcation in predator–prey model with stocking and harvesting

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-10-23 DOI: 10.1002/mma.10559

Ranchao Wu, Luzi Chen

引用次数: 0

Leibniz rule for the high q-derivatives of a quotient of two functions

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-10-21 DOI: 10.1002/mma.10558

Predrag M. Rajković, Dragan S. Rakić, Sladjana D. Marinkovic

{"title":"Leibniz rule for the high \u0000q-derivatives of a quotient of two functions","authors":"Predrag M. Rajković, Dragan S. Rakić, Sladjana D. Marinkovic","doi":"10.1002/mma.10558","DOIUrl":"https://doi.org/10.1002/mma.10558","url":null,"abstract":"In this paper, we introduce some explicit and recursive formulas for the \u0000<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$$ n $$</annotation>\u0000 </semantics></math>th \u0000<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$$ q $$</annotation>\u0000 </semantics></math>-derivative of a quotient of two functions. We establish the connections between linear algebra, the homomorphisms between commutative algebras and the properties of \u0000<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$$ q $$</annotation>\u0000 </semantics></math>-differential operator. One of the formulas involves the determinant of the functions and their \u0000<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$$ q $$</annotation>\u0000 </semantics></math>-derivatives. Then, we show that the formulas in the classical mathematical analysis are their special cases. Finally, we used formulas to obtain some interesting \u0000<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$$ q $$</annotation>\u0000 </semantics></math>-identities.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4477-4493"},"PeriodicalIF":2.1,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Inverse problems of the wave equation for media with mixed but separated heterogeneous parts

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-10-21 DOI: 10.1002/mma.10537

Mishio Kawashita, Wakako Kawashita

{"title":"Inverse problems of the wave equation for media with mixed but separated heterogeneous parts","authors":"Mishio Kawashita, Wakako Kawashita","doi":"10.1002/mma.10537","DOIUrl":"https://doi.org/10.1002/mma.10537","url":null,"abstract":"In this article, the inverse problems for the wave equation in a medium in which multiple types of cavities and inclusion exist in a mixture are considered. From the point of view of the indicator function of the enclosure method, there are two types of heterogeneous parts: “minus group” and “plus group.” For example, cavities with the Dirichlet boundary condition belong to the minus group, while inclusions with smaller propagation velocity belong to the plus group. The heterogeneous part of the minus group gives a negative sign to the indicator function, and the heterogeneous part of the plus group gives a positive sign. In general, the presence of many types of heterogeneous parts causes cancelation of the sign of the indicator function. Such cases are referred to as “mixed cases.” Here, we consider the case that the shortest length obtained from the indicator function is attained only by heterogeneous parts of the same group. This case is called the “mixed but separated case,” and it is shown that the method of elliptic estimates developed by Ikehata works well. We also show that the case of a two-layered background medium with a flat layer can be considered in the same way as the case of a homogeneous background medium.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4144-4172"},"PeriodicalIF":2.1,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10537","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Global existence and boundedness in a two-dimensional parabolic chemotaxis system with competing attraction and repulsion effects

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-10-21 DOI: 10.1002/mma.10550

Bruno Telch, Genyle Nascimento

{"title":"Global existence and boundedness in a two-dimensional parabolic chemotaxis system with competing attraction and repulsion effects","authors":"Bruno Telch, Genyle Nascimento","doi":"10.1002/mma.10550","DOIUrl":"https://doi.org/10.1002/mma.10550","url":null,"abstract":"In this paper, we investigate a chemotaxis system under homogeneous Neumann boundary conditions within a bounded domain with a smooth boundary. The system describes the movement of cells in response to two chemical signal substances: one acts as a chemoattractant, while the other serves as a chemorepellent, both produced by the cells. The system takes into account chemotactic sensitivity in the reaction movement when detecting these chemicals. Under certain assumptions, we demonstrate the existence of a unique global bounded classical solution for the proposed problem. To further understand the time evolution of the system's solutions, we conduct numerical experiments and analyze the dynamic properties of the \u0000<math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ {L}&amp;amp;#x0005E;{infty}left(Omega right) $$</annotation>\u0000 </semantics></math> norm of the solutions with respect to variations in chemical production rates.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4332-4343"},"PeriodicalIF":2.1,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0