Detecting alternative attractors in ecosystem dynamics

Detecting shifts in nonlinear dynamics using Empirical Dynamic Modeling with Nested-Library Analysis

Abrupt changes in system states and dynamical behaviors are often observed in natural systems; such phenomena, named regime shifts, are explained as transitions between alternative steady states (more generally, attractors). Various methods have been proposed to detect regime shifts from time series data, but a generic detection method with theoretical linkage to underlying dynamics is lacking. Here, we provide a novel method named Nested-Library Analysis (NLA) to retrospectively detect regime shifts using empirical dynamic modeling (EDM) rooted in theory of attractor reconstruction. Specifically, NLA determines the time of regime shift as the cutting point at which sequential reduction of the library set (i.e., the time series data used to reconstruct the attractor for forecasting) optimizes the forecast skill of EDM. We illustrate this method on a chaotic model of which changing parameters present a critical transition. Our analysis shows that NLA detects the change point in the model system and outperforms existing approaches based on statistical characteristics. In addition, NLA empirically detected a real-world regime shift event revealing an abrupt change of Pacific Decadal Oscillation index around the mid-1970s. Importantly, our method can be easily generalized to various systems because NLA is equation-free and requires only a single time series.

Usefulness and limitations of convergent cross sorting and continuity scaling methods for their application in simulated and real-world time series

Causality detection methods are valuable tools for detecting causal links in complex systems. The efficiency of continuity scaling (CS) and the convergent cross sorting (CSS) methods to detect causality was analysed. Usefulness and limitations of both methods in their application to simulated and real-world time series was explored under different scenarios. We find that CS is more robust and efficient than the CSS method for all simulated systems, even when increasing noise levels were considered. Both methods were not able to infer causality when time series with a marked difference in their main frequencies were analysed. Minimum time-series length required for the detection of a causal link depends on intrinsic system dynamics and on the method selected to detect it. Using simulated time series, only the CS method was capable to detect bidirectional causality. Causality detection, using the CS method, should at least include: (i) causality strength convergence analysis, (ii) statistical tests of significance, (iii) time-series standardization, and (iv) causality strength ratios as a strength indicator of relative causality between systems. Causality cannot be detected by either method in simulated time series that exhibit generalized synchronization.

Bifurcation, chaos, multistability, and organized structures in a predator-prey model with vigilance

There is not a single species that does not strive for survival. Every species has crafted specialized techniques to avoid possible dangers that mostly come from the side of their predators. Survival instincts in nature led prey populations to develop many anti-predator strategies. Vigilance is a well-observed effective antipredator strategy that influences predator-prey dynamics significantly. We consider a simple discrete-time predator-prey model assuming that vigilance affects the predation rate and the growth rate of the prey. We investigate the system dynamics by constructing isoperiodic and Lyapunov exponent diagrams with the simultaneous variation of the prey's growth rate and the strength of vigilance. We observe a series of different types of organized periodic structures with different kinds of period-adding phenomena. The usual period-bubbling phenomenon is shown near a shrimp-shaped periodic structure. We observe the presence of double and triple heterogeneous attractors. We also notice Wada basin boundaries in the system, which is quite rare in ecological systems. The complex dynamics of the system in biparameter space are explored through extensive numerical simulations.