Coupled Map Lattice based Homeostatic Complex Systems

Abstract

Homeostasis is the ability to regulate the essential variables of a complex system within a viability zone in the face of perturbations. It is a core complexity phenomenon for understanding real or artificial life. In this thesis, we explore the interplay betweennonlinear system dynamics and complex topologies in such homeostatic (self-regulating) systems.

We investigate the self-causing nature of homeostasis in artificial and real-world complex systems. We analyse planetary and ecological homeostasis using daisyworld system – a cybernetic proof of Gaia hypothesis and apply those principles to demonstrate the social homeostasis in stock market. We reconstruct the formulations of the original daisyworld based on Coupled Map Lattice (CML) which enable us to investigate a wide range of rich features of complex systems covering different arenas such as system science, nonlinear science and network science.

Our study reveals that daisyworld is a self-oganizing system and a reaction-diffusion (activator-inhibitor) system exhibiting an array of fascinating pattern formations – complex patterns, Turing-like structures, cyclic patterns, random patterns and uniform dispersed patterns for different parameter settings. The phenomenon governing the self-organizing pattern formation in our system is observed in biological systems (schooling of fish, animal coat formation, etc.) as well as in non-living systems (Turings reaction-diffusion system, Belousov-Zhabotinsky reaction, B ́nard convection, etc.).

We incorporate evolutionary interactions in our system via replicator-mutator mechanisms. The results underline the importance of balance between ecosystem feedback and ecosystem disturbance in generating spatially coexistence of domains of dominance among the original daisies and their mutants and adaptants.

We inspect our system based on small-world graphs (complex topologies) embodying realistic couplings via the Watts-Strogatz (WS), Newman-Watts models and Smallest-world (SW) models. We examine our system on an adaptive topology (adding connections with more realistic mechanisms) where there exists a feedback between the local dynamics and the topology. We introduce scale-freeness into our system with high clustering.We thus perturb our system through system parameters, system topologies and evolutionary changes. In all scenarios, our system self-regulates the environment and thus life persists, and thereby demonstrating robustness. We also introduce metrics Morans I and permutation entropy to measure the spatio-temporal dynamics of the system.

Our remarkable finding is that by applying the dynamical linking mechanisms to our system on regular lattice can self-organise to a lattice with small-world phenomenon. We observe completely coherent (homogeneous) short-lived cyclical dominance even with a small fraction of long-range couplings in complex and adaptive topologies. This apparent behaviour is seen in social, political and economical realms.

Our system yields profound insights and implications, from which we derive an analogy with stock market. Based on an Ecosystem Approach, we analyse the feedback between market sentiment and stock price. We collect $APPL tweets from twitter and stock datafrom Yahoo finance and demonstrate their homeostatic nature. We compare stock market with other social homeostatic systems in nature such as termite colonies. Thus our study on self-causing systems helps both in understanding existing self-regulating systems and in modelling new artificial homeostatic system.