Communications in Nonlinear Science and Numerical Simulation最新文献

英文中文

Finite-time contractive stabilization for fractional-order switched systems via event-triggered impulse control

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-06 DOI: 10.1016/j.cnsns.2025.108658

P. Gokul , Ardak Kashkynbayev , M. Prakash , Rakkiyappan Rajan

This article investigates the issue of finite-time stabilization for fractional-order switched nonlinear system (FOSNS) under the novel framework of mode-dependent event-triggered mechanism (MDETM). Initially, this study effectively addresses Zeno behavior (ZB) avoidance in FOSNS by the MDETM approach. This mechanism operates through the strategy of event-triggered impulsive control (ETIC) and the constraint of mode-specific average dwell time. Following this, we establish finite-time stability (FTS) and finite-time contractive stability (FTCS) for general FOSNS by employing the Lyapunov-based methodology. This approach is employed to analyze situations where the fractional derivatives of Lyapunov functions (LFs) of the modes are indefinite. Furthermore, the criteria of ZB, FTS, and FTCS are validated for application of FOSNS that adheres to the same framework as proposed for general FOSNS. The utilization of linear matrix inequality (LMI) was employed to derive the control gain matrix, ensuring the preservation of the stability property. To conclude, the efficacy of the introduced ETIC strategies is demonstrated through the analysis of two illustrative examples.

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引用次数: 0

Two lower boundedness-preservity auxiliary variable methods for a phase-field model of 3D narrow volume reconstruction

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-05 DOI: 10.1016/j.cnsns.2025.108649

Xiangjie Kong, Renjun Gao, Boyi Fu, Dongting Cai, Junxiang Yang

Three-dimensional (3D) volume reconstruction remains a fundamental technique with wide applications in fields such as 3D printing, medical diagnostics, and industrial design. This paper presents two novel lower boundedness-preserving auxiliary variable methods designed for the phase-field model of 3D narrow volume reconstruction. By employing scattered point data, our approach reconstructs smooth narrow volumes using a phase-field Allen–Cahn model with a control function. The proposed method ensures energy dissipation and smooth surface throughout the reconstruction process. By introducing an auxiliary variable, the nonlinear term in the governing equation is reformulated, allowing for efficient time-marching schemes. The fully discrete scheme is linear, and its unconditional stability is rigorously estimated. Numerical experiments are conducted to demonstrate the energy stability, accuracy, and effectiveness of our proposed methods in various 3D reconstruction tasks, establishing its broad applicability.

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引用次数: 0

Traveling waves in a generalized Bogoyavlenskii coupled system under perturbation of distributed delay and weak dissipation

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-05 DOI: 10.1016/j.cnsns.2025.108647

Feiting Fan , Xingwu Chen

In this paper, we focus on the traveling waves for a perturbed generalized Bogoyavlenskii coupled system with delay convection term and weak dissipation, including periodic waves, solitary waves, kink and anti-kink waves. The corresponding traveling wave equation can be transformed into a 4-dimensional dynamical system, which is regarded as a singularly perturbed system and is reduced to a near-Hamiltonian form. We construct a locally invariant manifold diffeomorphic to the critical manifold with normally hyperbolicity and then give the existence conditions of traveling waves by the geometric singular perturbation theory as well as the number of periodic waves by analyzing the monotonicity of ratios of Abelian integrals. Moreover, the monotonicity of the wave speed is provided as well as its supremum and infimum. Numerical simulations are in complete agreement with the theoretical predictions.

引用次数: 0

Crossing limit cycles in piecewise smooth Kolmogorov systems: An application to Palomba’s model

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-05 DOI: 10.1016/j.cnsns.2025.108646

Yagor Romano Carvalho , Luiz F.S. Gouveia , Oleg Makarenkov

In this paper, we study the number of isolated crossing periodic orbits, so-called crossing limit cycles, for a class of piecewise smooth Kolmogorov systems defined in two zones separated by a straight line. In particular, we study the number of crossing limit cycles of small amplitude. They are all nested and surround one equilibrium point or a sliding segment. We denote by

M_{p_{K}}^{c} (n)

the maximum number of crossing limit cycles bifurcating from the equilibrium point via a degenerate Hopf bifurcation for a piecewise smooth Kolmogorov systems of degree

n = m + 1

. We make a progress towards the determination of the lower bounds

M_{K}^{p} (n)

of crossing limit cycles bifurcating from the equilibrium point via a degenerate Hopf bifurcation for a piecewise smooth Kolmogorov system of degree

n

. Specifically, we shot that

M_{p_{K}}^{c} (2) \geq 1

M_{p_{K}}^{c} (3) \geq 12

, and

M_{p_{K}}^{c} (4) \geq 18

. In particular, we show at least one crossing limit cycle in Palomba’s economics model, considering it from a piecewise smooth point of view. To our knowledge, these are the best quotes of limit cycles for piecewise smooth polynomial Kolmogorov systems in the literature.

{"title":"Crossing limit cycles in piecewise smooth Kolmogorov systems: An application to Palomba’s model","authors":"Yagor Romano Carvalho , Luiz F.S. Gouveia , Oleg Makarenkov","doi":"10.1016/j.cnsns.2025.108646","DOIUrl":"10.1016/j.cnsns.2025.108646","url":null,"abstract":"<div><div>In this paper, we study the number of isolated crossing periodic orbits, so-called crossing limit cycles, for a class of piecewise smooth Kolmogorov systems defined in two zones separated by a straight line. In particular, we study the number of crossing limit cycles of small amplitude. They are all nested and surround one equilibrium point or a sliding segment. We denote by <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow><mrow><mi>c</mi></mrow></msubsup><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> the maximum number of crossing limit cycles bifurcating from the equilibrium point via a degenerate Hopf bifurcation for a piecewise smooth Kolmogorov systems of degree <span><math><mrow><mi>n</mi><mo>=</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></math></span>. We make a progress towards the determination of the lower bounds <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><mi>K</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> of crossing limit cycles bifurcating from the equilibrium point via a degenerate Hopf bifurcation for a piecewise smooth Kolmogorov system of degree <span><math><mi>n</mi></math></span>. Specifically, we shot that <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow><mrow><mi>c</mi></mrow></msubsup><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mo>≥</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow><mrow><mi>c</mi></mrow></msubsup><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>≥</mo><mn>12</mn></mrow></math></span>, and <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow><mrow><mi>c</mi></mrow></msubsup><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow><mo>≥</mo><mn>18</mn></mrow></math></span>. In particular, we show at least one crossing limit cycle in Palomba’s economics model, considering it from a piecewise smooth point of view. To our knowledge, these are the best quotes of limit cycles for piecewise smooth polynomial Kolmogorov systems in the literature.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108646"},"PeriodicalIF":3.4,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Exponential stability estimate for derivative nonlinear Schrödinger equation

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-01 DOI: 10.1016/j.cnsns.2025.108644

Xue Yang

We consider the derivative nonlinear Schrödinger equations

i u_{t} = - u_{x x} + V * u + i \partial_{x} (\partial_{\bar{u}} F (u, \bar{u})), x \in T

with a nonlinearity

F (u, \bar{u})

of order at least

3

at the origin. We prove that for almost all

V

, if the initial data is

ɛ

-small in the modified Sobolev space, the solution is stable over time intervals of order

ɛ^{- \frac{1}{ɛ}} \cdot e^{e^{\frac{1}{ɛ}}}

. Our findings extend the stability time

e^{\frac{(ln ɛ)}{ɛ}}

introduced by Cong (2022) to

e^{e^{\frac{1}{ɛ}}}

引用次数: 0

Limit cycle bifurcations in a class of piecewise Hamiltonian systems

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-01 DOI: 10.1016/j.cnsns.2025.108643

Wenwen Hou, Maoan Han

In this paper, we first obtain explicit expressions of up to fourth order Melnikov functions for a class of piecewise Hamiltonian systems with two zones separated by two semi-straight lines. Then based on these expressions, we give upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise linear system under piecewise polynomial perturbations. The upper bounds are sharp for some cases of lower degrees.

引用次数: 0

The Cauchy matrix structure and solutions of the three-component mKdV equations

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-01 DOI: 10.1016/j.cnsns.2024.108456

Mengli Tian , Chunxia Li , Yehui Huang , Yuqin Yao

Starting from a 4 × 4 matrix Sylvester equation, the matrix mKdV system as an unreduced equation is worked out and the explicit expression of its solution is presented by applying the Cauchy matrix method. Then, two kinds of reduction conditions are given, under which the complex three-component mKdV(CTC-mKdV) equation and the real three-component mKdV(RTC-mKdV) equation can be obtained, and finally, the explicit expressions of soliton solution and Jordan block solution for CTC-mKdV equation and RTC-mKdV equation are presented, respectively. Specially, the generated conditions of one-soliton solutions, two-soliton solutions, double-pole solutions, symmetry broken solutions and soliton molecule are presented, and their dynamic behaviors were analyzed.

从 4 × 4 矩阵西尔维斯特方程出发，运用考奇矩阵法计算出未还原方程的矩阵 mKdV 系统，并给出其解的显式表达。然后，给出了两种还原条件，在这两种条件下可以得到复三元 mKdV（CTC-mKdV）方程和实三元 mKdV（RTC-mKdV）方程，最后分别给出了 CTC-mKdV 方程和 RTC-mKdV 方程的孤子解和约旦块解的显式。特别是给出了单孤子解、双孤子解、双极解、对称破缺解和孤子分子的生成条件，并分析了它们的动力学行为。

引用次数: 0

Efficient detection of chaos through the computation of the Generalized Alignment Index (GALI) by the multi-particle method

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-01 DOI: 10.1016/j.cnsns.2025.108635

Bertin Many Manda , Malcolm Hillebrand , Charalampos Skokos

We present a method for the computation of the Generalized Alignment Index (GALI), a fast and effective chaos indicator, using a multi-particle approach that avoids variational equations. We show that this approach is robust and accurate by deriving a leading-order error estimation for both the variational (VM) and the multi-particle (MPM) methods, which we validate by performing extensive numerical simulations on two prototypical models: the two degrees of freedom Hénon-Heiles system and the multidimensional

β

-Fermi-Pasta–Ulam-Tsingou chain of oscillators. The dependence of the accuracy of the GALI on control parameters such as the renormalization time, the integration time step and the deviation vector size is studied in detail. We test the MPM implemented with double precision accuracy (

ɛ \approx 1 0^{- 16}

) and find that it performs reliably for deviation vector sizes

d_{0} \approx ɛ^{1 / 2}

, renormalization times

τ ≲ 1

, and relative energy errors

E_{r} ≲ ɛ^{1 / 2}

. These results hold for systems with many degrees of freedom and demonstrate that the MPM is a robust and efficient method for studying the chaotic dynamics of Hamiltonian systems. Our work makes it possible to explore chaotic dynamics with the GALI in a vast number of systems by eliminating the need for variational equations.

{"title":"Efficient detection of chaos through the computation of the Generalized Alignment Index (GALI) by the multi-particle method","authors":"Bertin Many Manda , Malcolm Hillebrand , Charalampos Skokos","doi":"10.1016/j.cnsns.2025.108635","DOIUrl":"10.1016/j.cnsns.2025.108635","url":null,"abstract":"<div><div>We present a method for the computation of the Generalized Alignment Index (GALI), a fast and effective chaos indicator, using a multi-particle approach that avoids variational equations. We show that this approach is robust and accurate by deriving a leading-order error estimation for both the variational (VM) and the multi-particle (MPM) methods, which we validate by performing extensive numerical simulations on two prototypical models: the two degrees of freedom Hénon-Heiles system and the multidimensional <span><math><mi>β</mi></math></span>-Fermi-Pasta–Ulam-Tsingou chain of oscillators. The dependence of the accuracy of the GALI on control parameters such as the renormalization time, the integration time step and the deviation vector size is studied in detail. We test the MPM implemented with double precision accuracy (<span><math><mrow><mi>ɛ</mi><mo>≈</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>16</mn></mrow></msup></mrow></math></span>) and find that it performs reliably for deviation vector sizes <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≈</mo><msup><mrow><mi>ɛ</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span>, renormalization times <span><math><mrow><mi>τ</mi><mo>≲</mo><mn>1</mn></mrow></math></span>, and relative energy errors <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>≲</mo><msup><mrow><mi>ɛ</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span>. These results hold for systems with many degrees of freedom and demonstrate that the MPM is a robust and efficient method for studying the chaotic dynamics of Hamiltonian systems. Our work makes it possible to explore chaotic dynamics with the GALI in a vast number of systems by eliminating the need for variational equations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108635"},"PeriodicalIF":3.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143257792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Qualitative theoretical research on solutions of fractional switched systems with variable-time switching mechanism

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-01-30 DOI: 10.1016/j.cnsns.2025.108645

Zeming Zhao , Yunfei Peng

This paper is devoted to the qualitative theory of a class of fractional switched systems with a variable-time switching mechanism (FSSVT). FSSVT is a new class of state-feedback fractional switched systems, where the active regions of each subsystem vary with time. Initially, we obtain the condition of the existence and uniqueness of the global solution for FSSVT and give a criterion for determining the number of switching. Subsequently, by introducing a topology constructed from the approximate solutions of FSSVT, we obtain the continuous dependence and Gâteaux differentiability of solutions with respect to initial values in a weak sense. Finally, we investigate the periodicity of solutions for FSSVT and provide an example.

引用次数: 0

Practical fixed-time consensus for continuous action iterated dilemmas under communication and learning constraints

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-01-30 DOI: 10.1016/j.cnsns.2025.108642

Hasnain Ali , Syed Muhammad Amrr

This paper introduces a continuous action iterated dilemma (CAID) model, enabling agents to adopt a spectrum of strategies beyond the traditional game theory practice of having only binary options. Existing research on the CAID problem often overlooks real-world challenges and assumes perfect communication and learning rates among agents. This work considers the limitations of complex networks, such as communication delays, restricted learning rates of agents, dynamic uncertainty, and information losses during data transmission. The proposed strategy employs a fixed-time convergent algorithm with Artstein transformation that transforms a delay-induced system into a delay-free model, and the fixed-time design ensures consensus among all agents within a fixed and bounded timeframe, regardless of the initial conditions. The convergence analysis of the proposed CAID strategy is conducted using Lyapunov theory, validating the practical fixed-time convergence of consensus despite communication delays, confined learning rates, model uncertainty, and information loss. Numerical simulations under varying conditions demonstrate that the proposed approach facilitates faster consensus attainment and requires fewer iterations than the existing method.

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引用次数: 0

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