Stability, resilience, and collective dynamics in networks of biological systems

Abstract

Many interacting dynamical systems ranging from ecosystems to neuronal systems can be modeled using complex networks. In complex networks, the dynamical properties of an uncoupled node and the interaction topology between nodes are two critical determinants of network dynamics. Therefore, a variation in node dynamics and/or network topology results in several interesting collective dynamics, including synchronization and cascading failures. The occurrence of synchronization in population abundance is known to influence population persistence and is an important research topic. Similarly, cascading failure in networks can trigger sudden collapse or tipping points in many natural systems. This thesis investigates synchronization, stability, and resilience properties of different complex networks. We study how time-varying species interactions in an ecological network affect synchrony patterns. We identify the condition for which the synchronization state will be stable using the master stability function and by computing the basin stability. Most seasonally forced ecosystems consider forcing with a fixed frequency; in contrast, we study the dynamics of a driven spatial ecological network with frequency modulation. With an increase in the strength of frequency modulation, the region of stable synchronous solution increases in the parameter space. We show that the phase reduction method can help to distinguish intermittent synchrony from synchrony and asynchrony. Next, we develop a bio-energetic model of mutualistic networks. We show that the system can experience sudden community collapse with temperature variations. Further, by using a dimension reduction method, we study the stability of the considered network. We mitigate sudden network collapse and study how network structural properties affect such mitigation policies. Cooperative interspecific competition, a widely observed behavior among individuals at different levels, can be modeled using evolutionary game theory. Species can change their strategy due to population feedback or varying resource availability. We incorporate an adaptive species strategy within a higher dimensional Lotka-Volterra system. We find that adaptive strategy results in increased species persistence across various games and network structures. Another less explored area in complex networks is the loss of resilience in the presence of nonequilibrium dynamics. In this thesis, we report that the percentage of nodes exhibiting nonequilibrium dynamics plays a vital role in determining a network’s resilience against environmental stress, irrespective of its topology. Additionally, we identify a covariance-based early warning signal to forecast network tipping points.