Quantized Dissensus in Networks of Agents subject to Death and Duplication

Dissensus is a modeling framework for networks of dynamic agents in competition for scarce resources. Originally inspired by biological cells behaviors, it fits also marketing, finance and many other application areas. Competition is often unstable in the sense that strong agents, those having access to large resources, gain more and more resources at the expense of weak agents. Thus, strong agents duplicate when reaching a critical amount of resources, whereas weak agents die when loosing all their resources. To capture all these phenomena we introduce systems with a discrete time gossip and unstable state dynamics interrupted by discrete events affecting the network topology. Invariancy of states and topologies and network connectivity are explored.