Integrability and dynamics of a low-dimensional model for glacial cycle: The effect of CO2 concentration

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-03-26 DOI:10.1016/j.cnsns.2025.108781

Shuangling Yang

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引用次数: 0

Abstract

The Saltzman–Sutera model is a simplified system of ordinary differential equations that captures the essential dynamics of Earth’s glacial cycles over the past two million years. Despite its simplicity, the model accounts for significant climate phenomena. In this paper, we rigorously investigate the integrability and dynamics of the Saltzman–Sutera model. (i) First, we demonstrate the non-existence of integral of motions, confirming the absence of closed-form solutions. (ii) Next, we conduct a bifurcation analysis, identifying various stability transitions, including pitchfork bifurcation, (degenerate) Hopf bifurcation and

Z_{2}

-symmetric Bogdanov–Takens bifurcations of codimension two. (iii) Finally, through the Poincaré compactification, we explore the system’s behavior at infinity, revealing a conservative vector field structure. Our findings offer a better understanding of the internal climate dynamics that influence Earth’s ice age cycles.

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冰期旋回低维模式的可积性与动力学：CO2浓度的影响

萨尔茨曼-苏特拉模型是一个简化的常微分方程系统，它捕捉了过去200万年地球冰川循环的基本动力学。尽管它很简单，但该模式解释了重要的气候现象。本文研究了Saltzman-Sutera模型的可积性和动力学性质。(1)首先，我们证明了运动积分的不存在性，证实了闭型解的不存在性。（ii）接下来，我们进行了分岔分析，识别了各种稳定性转变，包括pitchfork分岔，（简并）Hopf分岔和z2 -对称Bogdanov-Takens分岔。（iii）最后，通过poincar紧化，我们探索了系统在无穷远处的行为，揭示了一个保守的向量场结构。我们的发现对影响地球冰期周期的内部气候动力学提供了更好的理解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.