By David P. Rosin
This thesis makes a speciality of the dynamics of self reliant Boolean networks, at the foundation of Boolean common sense capabilities in non-stop time with no exterior clocking. those networks are learned with built-in circuits on an digital chip as a box programmable gate array (FPGA) with approximately 100,000 common sense gates, delivering a really versatile version approach. It permits quick and inexpensive layout cycles and massive networks with arbitrary topologies and coupling delays.
The writer provides pioneering effects on theoretical modeling, experimental cognizance, and chosen purposes. during this regard, 3 sessions of novel dynamic habit are investigated: (i) Chaotic Boolean networks are proposed as high-speed actual random quantity turbines with excessive bit premiums. (ii) Networks of periodic Boolean oscillators are domestic to long-living brief chimera states, i.e., novel styles of coexisting domain names of spatially coherent (synchronized) and incoherent (desynchronized) dynamics. (iii) Excitable networks show cluster synchronization and will be used as quick man made Boolean neurons whose spiking styles may be managed. This paintings provides the 1st experimental platform for giant complicated networks, for you to facilitate interesting destiny developments.
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Additional resources for Dynamics of Complex Autonomous Boolean Networks
On the other hand, because Kauffman networks are finite-state machines, all orbits are closed and periodic, which violates one condition for deterministic chaos. I discuss deterministic chaos and its requirements in detail in Sect. 1. The periods can, however, be as long as T = 10150 iterations for N -K networks of N = 103 nodes and in-degrees of K = N . Kauffman networks can display a dynamical transition to such long trajectories with exponential growth of the Hamming distance. The dynamical instability has implications for biology because Kauffman proposed that different attractors in Boolean networks correspond to different cell types of organisms .
Furthermore, Kauffman’s description does not include continuous-time interactions and finite transmission delays between nodes. Time delays have been proven to play a crucial role for the dynamics in many systems because they lead to an infinite-dimensional phase space. For example, time delays can dictate the periodicity of oscillations and stabilize and destabilize fixed points and periodic orbits [11–17]. 2 Boolean Delay Equations Ghil and Mullhaupt introduced Boolean delay equations as an autonomous Boolean network model .
T. : Chaotic dynamics in an electronic model of a genetic network. J. Stat. Phys. 121, 969 (2005) 30. S. J. S. Socolar, R. Zhang, On the origin of chaos in autonomous Boolean networks. Phil. Trans. R. Soc. A 368, 495 (2010) Chapter 3 Autonomous Boolean Networks on Electronic Chips Abstract In this chapter, I discuss the experimental implementation of autonomous Boolean networks on electronic chips. Specifically, I describe the setup and nonideal characteristics of the used microelectronic chips in Sect.