Global history, the emergence of chaos and inducing sustainability in networks of socio-ecological systems

Abstract

In this study, we propose a simplified model of a socio-environmental system that accounts for population, resources, and wealth, with a quadratic population contribution in the resource extraction term. Given its structure, an analytical treatment of attractors and bifurcations is possible. In particular, a Hopf bifurcation from a stable fixed point to a limit cycle emerges above a critical value of the extraction rate parameter. The stable fixed-point attractor can be interpreted as a sustainable regime, and a large-amplitude limit cycle as an unsustainable regime. The model is generalized to multiple interacting systems, with chaotic dynamics emerging for small non-uniformities in the interaction matrix. In contrast to systems where a specific parameter choice or high dimensionality is necessary for chaos to emerge, chaotic dynamics here appears as a generic feature of the system. In addition, we show that diffusion can stabilize networks of sustainable and unsustainable societies, and thus, interconnection could be a way of increasing resilience in global networked systems. Overall, the multi-systems model provides a timescale of predictability (300-1000 years) for societal dynamics comparable to results from other studies, while indicating that the emergent dynamics of networks of interacting societies over longer time spans is likely chaotic and hence unpredictable.

Optimizing Nonlinear Variable Fractional Volta’s System Design with RBFNN-Enhanced Intelligence Computing Networks

“…The dynamical systems, an interdisciplinary field established in prehistoric celestial mechanics of astronomers and rectified by Newtonian physics in the 17th century, form a foundation for insight into the evolving dynamics of complex systems. On the far side of disentangle historical tapestry, these systems bear deep physical significance by exploring order in apparently chaotic behaviors, for affine control dynamical systems [1], affecting our understanding of celestial orbits [2], weather variations [3], mathematical economics [4], Planetary motion [5], health intimations [6], secure optical communication [7] and ecological system [8]. Dynamical systems have a broader impact on artificial intelligence, data science, and network theory [9].…”

The simplest 4-D autonomous hyperchaotic system coined: Theoretical analysis and analog circuit design

“…The interest in hyperchaotic systems is justified by their usefulness in a number of applications, such as secure communications, image encryption, and the generation of random signals [7][8][9]. Hyperchaemia has been reported in various types of systems, such as electronic circuits [10], coupled oscillator systems [11], neural networks [12], financial models [13], optical systems [14], chemical reactions [15], and ecological systems [16]. An autonomous hyperchaotic system of order m has at most m-2 positive Lyapunov exponents because there is always at least one zero Lyapunov exponent and one negative Lyapunov exponent.…”