Measuring Complexity in Reactor Networks with Cubic Autocatalytic Reactions

Abstract

Systems with high steady-state multiplicity and rich dynamic behavior are difficult to investigate using conventional reductionist methods. A network of more than five reactors hosting cubic autocatalytic reactions may potentially have more than 102 steady states and many distinct dynamic regimes, all for the same parameter set. This paper discusses how the static complexity of such systems can be measured to give a holistic picture. To achieve this, stochastic simulations were performed to statistically determine the bifurcation structure of the system, and the gathered information is summarized using a measure akin to fractal dimension. With this measure, the growth of static complexity is investigated as a function of the network size.

Agent-based system for reconfiguration of distributed chemical reactor network operation

“…Since the complexity of the system grows geometrically with the number of species and the number of reactors in the system [5], [7], for a network size of I > 3 with two or more species, analytical solutions become practically intractable, although a single trivial steady state (r i = 1, p in = 0) exists for all i for every combination of model parameter values. This trivial steady state is always stable and will always pose a threat to control efforts as it represents total extinction of the autocatalytic species in the system.…”

“…The topography of interconnected CSTR networks has been shown to drastically affect the steady state bifurcation structure of the system [5], [7]. Spatial inhomogeneity of the network can be increased by increasing the number of reactors in the network as well as manipulating the interconnection flow rates of the network.…”

Self-Organizing Agent-Based Grade Transition in Distributed Chemical Reactor Networks

“…Once the final configuration is found, the second sub problem is to decide on the actions to be taken in the correct order to move the system from its current state to the final state. Earlier works demonstrated autocatalytic reactions in CSTR networks to simulate population dynamics, multiple species of organisms that compete on same resources, or chemical manufacturing problems (Tatara et al, 2004;Tatara et al, 2005a;Tatara et al, 2005b). Controlling the spatial distribution of autocatalytic species that compete for the same resources in a network of reactors can be achieved by simultaneous manipulation of interconnection flow rates within the system.…”

Adaptive Agent-Based Control of Product Grade Transitions in Reactor Networks

“…Hybrid control systems that combine process dynamics and discrete control elements and include multiple models for different operating points are one way to develop control systems for spatially distributed systems (Morari et al, 2003;Christofides and El-Farra, 2005). An alternative approach is based on a hierarchical agent-based system with local and global control structures (Tatara et al, 2005c;Tatara et al, 2005b) that has been demonstrated on a network of interconnected continuous stirred tank reactors (CSTRs). Reactor networks exhibit highly complex behavior with multiple steady state operating regimes and have a large pool of candidates for manipulated variables (Tatara et al, 2004).…”