Network analysis of chaotic dynamics in fixed-precision digital domain

When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of a digital chaotic system, the dynamics can be transformed to the form of a state-mapping network. Then, the parameters of the network are verified by some typical dynamical metrics of the original chaotic system in infinite precision, such as Lyapunov exponent and entropy. This article reviews some representative works on the network-based analysis of digital chaotic dynamics and presents a general framework for such analysis, unveiling some intrinsic relationships between digital chaos and complex networks. As an example for discussion, the dynamics of a state-mapping network of the Logistic map in a fixed-precision computer is analyzed and discussed.Comment: 5 pages, 9 figure

Invariant set of weight of perceptron trained by perceptron training algorithm

In this paper, an invariant set of the weight of the perceptron trained by the perceptron training algorithm is defined and characterized. The dynamic range of the steady state values of the weight of the perceptron can be evaluated via finding the dynamic range of the weight of the perceptron inside the largest invariant set. Also, the necessary and sufficient condition for the forward dynamics of the weight of the perceptron to be injective as well as the condition for the invariant set of the weight of the perceptron to be attractive is derived

The Kinetic Basis of Self-Organized Pattern Formation

In his seminal paper on morphogenesis (1952), Alan Turing demonstrated that different spatio-temporal patterns can arise due to instability of the homogeneous state in reaction-diffusion systems, but at least two species are necessary to produce even the simplest stationary patterns. This paper is aimed to propose a novel model of the analog (continuous state) kinetic automaton and to show that stationary and dynamic patterns can arise in one-component networks of kinetic automata. Possible applicability of kinetic networks to modeling of real-world phenomena is also discussed.Comment: 8 pages, submitted to the 14th International Conference on the Synthesis and Simulation of Living Systems (Alife 14) on 23.03.2014, accepted 09.05.201

COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS

The ability to simulate a biological organism by employing a computer is related to the ability of the computer to calculate the behavior of such a dynamical system, or the "computability" of the system.* However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A conjecture is formulated that suggests the possibility of employing an algebraic-topological, "quantum" computer (Baianu, 1971b) for analogous and symbolic simulations of biological systems that may include chaotic processes that are not, in genral, either recursively or digitally computable. Depending on the biological network being modelled, such as the Human Genome/Cell Interactome or a trillion-cell Cognitive Neural Network system, the appropriate logical structure for such simulations might be either the Quantum MV-Logic (QMV) discussed in recent publications (Chiara, 2004, and references cited therein)or Lukasiewicz Logic Algebras that were shown to be isomorphic to MV-logic algebras (Georgescu et al, 2001)

Chaos From Switched-Capacitor Circuits: Discrete Maps

A special-purpose analog computer made of switched-capacitor circuits is presented for analyzing chaos and bifurcation phenomena in nonlinear discrete dynamical systems modeled by discrete maps *n + t = fan)-Experimental results are given for four switched-capacitor circuits described by well-known discrete maps; namely, the logistic map, the piecewise-linear unimodal (one-hump) map, the H é non map, and the Lozi map