The complexity of biochemical intracellular signal transduction networks has led to speculation that the high degree of interconnectivity that exists in these networks transforms them into an information processing network. To test this hypothesis directly, a large scale model was created with the logical mechanism of each node described completely to allow… (More)
This paper is an analytical study of Boolean networks. The motivation is our desire to understand the large, complicated, and interconnected pathways which comprise intracellular biochemical signal transduction networks. The simplest possible conceptual model that mimics signal transduction with sigmoidal kinetics is the n-node Boolean network each of whose… (More)
OBJECTIVE To investigate the nature of variability present in time series generated from gait parameters of two different age groups via a nonlinear analysis. DESIGN Measures of nonlinear dynamics were used to compare kinematic parameters between elderly and young females. BACKGROUND Aging may lead to changes in motor variability during walking, which… (More)
One way of coping with the complexity of biological systems is to use the simplest possible models which are able to reproduce at least some nontrivial features of reality. Although two value Boolean models have a long history in technology, it is perhaps a little bit surprising that they can also represent important features of living organizms. In this… (More)
This paper considers a simple Boolean network with N nodes, each node's state at time t being determined by a certain number k of parent nodes, which is fixed for all nodes. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. We make use of a Boolean rule that is a generalization of rule 126 of elementary… (More)
In this paper we study the nonchaotic and chaotic behavior of all 3D conservative quadratic ODE systems with five terms on the right-hand side and one nonlinear term (5-1 systems). We prove a theorem which provides sufficient conditions for solutions in 3D autonomous systems being nonchaotic. We show that all but five of these systems:(3.8a,b), (3.11b),… (More)
We show analytically that almost all three-dimensional dissipative quadratic systems of ordinary differential equations with a total of five terms on the right-hand side and one nonlinear term (namely 5-1 cases) are not chaotic except twenty one of them. Indeed we find nine systems that exhibit chaos, which were discovered by Sprott and Malasoma earlier.… (More)
The solution to a deceptively simple combinatorial problem on bit strings results in the emergence of a fractal related to the Sierpinski Gasket. The result is generalized to higher dimensions and applied to the study of global dynamics in Boolean network models of complex biological systems.