Cantisán Julia, Yanchuk Serhiy, Seoane Jesús M, Sanjuán Miguel A F, Kurths Jürgen
Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos Tulipán s/n, 28933 Móstoles, Madrid, Spain.
Department of Mathematics, Humboldt University Berlin, 12489 Berlin, Germany.
Phys Rev E. 2023 Aug;108(2-1):024203. doi: 10.1103/PhysRevE.108.024203.
A variation in the environment of a system, such as the temperature, the concentration of a chemical solution, or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point, the system can tip from one attractor to another (bifurcation-induced tipping). Typically, this stability exchange occurs at a parameter value beyond the bifurcation value. This is what we call, here, the shifted stability exchange. We perform a systematic study on how the shift is affected by the initial parameter value and its change rate. To that end, we present numerical simulations and partly analytical results for different types of bifurcations and different paradigmatic systems. We show that the nonautonomous dynamics can be split into two regimes. Depending on whether we exceed the numerical or experimental precision or not, the system may enter the nondeterministic or the deterministic regime. This is determined solely by the conditions of the drift. Finally, we deduce the scaling laws governing this phenomenon and we observe very similar behavior for different systems and different bifurcations in both regimes.
系统环境的变化，如温度、化学溶液浓度或磁场的出现，可能会导致其中一个参数发生漂移。如果该参数越过一个分岔点，系统可能会从一个吸引子翻转到另一个吸引子（分岔诱导翻转）。通常，这种稳定性交换发生在超过分岔值的参数值处。这就是我们在此所说的偏移稳定性交换。我们对偏移如何受初始参数值及其变化率的影响进行了系统研究。为此，我们给出了不同类型分岔和不同典型系统的数值模拟和部分解析结果。我们表明，非自治动力学可分为两种状态。取决于我们是否超过数值或实验精度，系统可能进入非确定性或确定性状态。这仅由漂移条件决定。最后，我们推导了控制这一现象的标度律，并且在两种状态下观察到不同系统和不同分岔具有非常相似的行为。
