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Rate and memory effects in bifurcation-induced tipping
Julia Cantisán1, Serhiy Yanchuk2,3, Jesús M Seoane1
1Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos Tulipán s/n, 28933 Móstoles, Madrid, Spain.
Environmental changes can cause systems to abruptly shift states (bifurcation-induced tipping). This study reveals how initial conditions and drift rates influence this phenomenon, identifying deterministic and nondeterministic tipping regimes.
Area of Science:
- Complex systems dynamics
- Nonlinear dynamics and chaos theory
Background:
- Environmental variations can induce parameter drift in systems.
- When a parameter crosses a bifurcation point, systems can transition between states (bifurcation-induced tipping).
- This stability exchange often occurs beyond the critical bifurcation value, termed shifted stability exchange.
Purpose of the Study:
- To systematically investigate the factors influencing shifted stability exchange.
- To analyze the impact of initial parameter values and drift rates on bifurcation-induced tipping.
- To explore the emergence of deterministic and nondeterministic tipping regimes.
Main Methods:
- Numerical simulations of paradigmatic systems undergoing different bifurcation types.
- Analytical investigations into the dynamics of parameter drift.
- Analysis of system behavior under varying initial conditions and drift rates.
Main Results:
- Shifted stability exchange is shown to be dependent on initial parameter value and drift rate.
- Nonautonomous dynamics are categorized into two regimes: deterministic and nondeterministic.
- The tipping regime is determined by whether numerical or experimental precision thresholds are exceeded.
- Scaling laws governing the phenomenon were deduced, exhibiting consistent behavior across systems and bifurcations.
Conclusions:
- The study elucidates the mechanisms and influencing factors of bifurcation-induced tipping.
- A clear distinction between deterministic and nondeterministic tipping regimes is established based on drift conditions.
- Universality in the observed scaling laws suggests broad applicability across diverse complex systems.
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