In the fields of complex dynamics and complex networks, the inverse problem is generally regarded as hard and extremely challenging mathematically as complex dynamical systems and networks consists of a large number of interacting units. However, our ideas based on compressive sensing, in combination with innovative approaches, generates a new paradigm that offers the possibility to address the fundamental inverse problem in complex dynamics and networks. In particular, in this talk, I will argue that evolutionary games model, a common type of interactions in a variety of complex, networked, natural systems and social systems, allows the uncovering of the interacting structure of the underlying network and the understanding of its collective dynamics from small amounts of data. The method is validated by conducting an actual experiment to reconstruct a social network. Based on ecological real-world networks, I will discuss the interplay between transients and stochasticity in empirical mutualistic networks. Focusing on the tipping-point dynamics, I will discuss the phenomena of noise-induced collapse and noise-induced recovery. Two types of noise are considered, environmental (Gaussian white) noise and state-dependent demographic noise. I will also discuss control strategies that delay the extinction and advances the recovery by controlling the decay rate of pollinators in the stochastic mutualistic complex network. The phenomena of noise-induced collapse and recovery and the associated scaling laws, and the control of tipping point strategies have implications to managing high-dimensional ecological systems.
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Data based identification and prediction of nonlinear and complex dynamical systems, W.-X. Wang, Y.-C. Lai, and C. Grebogi, Phys. Reports 644, 1-76 (2016)
Predicting catastrophe in nonlinear dynamical systems by compressive sensing, W.-X. Wang, R. Yang, Y.-C. Lai, V. Kovanis, and C. Grebogi, Phys. Rev. Lett. 106, 154101 (2011)
Network reconstruction based on evolutionary-game data via compressive sensing, W.-X. Wang, Y.-C. Lai, C. Grebogi, and J. Ye, Phys. Rev. X 1, 021021 (2011)
Predicting tipping points in mutualistic networks through dimension reduction, J. Jiang, Z.-G. Huang, T.P. Seager, W. Lin, C. Grebogi, A. Hastings, and Y.-C. Lai, PNAS (Proc. Nat. Acad. Sci.) 115, E639-E647 (2018)
Noise-enabled species recovery in the aftermath of a tipping point, Y. Meng, J. Jiang, C. Grebogi, and Y.-C. Lai, Phys. Rev. E 101, 012206 (2020)
Tipping point and noise-induced transients in ecological networks, Y. Meng, Y.-C. Lai, and C. Grebogi, J. Royal Soc. Interface 17, 20200645 (2020)
Control of tipping points in stochastic mutualistic complex networks, Y. Meng and C. Grebogi, Chaos 31, 023118 (2021)
Sudden regime shifts after apparent stasis: Comment on long transients in Ecology, C. Grebogi, Physics of Life Reviews 32, 41 (2020)