We review the basic patterns of complex non-uniqueness in simple discrete-time population dynamics models. We begin by studying a population dynamics model of a single species with a two-stage, two-habitat life cycle. We then explore in greater detail two ecological models describing host–macroparasite and host–parasitoid interspecific interactions. In general, several types of attractors, e.g....

This paper investigates an approach to begin the study of fractals in architectural design. Vector-based fractals are studied to determine if the modification of vector direction in either the generator or the initiator will develop alternate fractal forms. The Koch Snowflake is used as the demonstrating fractal. Introduction A fractal is an object or quantity that displays self-similarity on a...

We consider classes of sets of r-adic expansions of reals speciied by means of the theory of formal languages or automata theory. It is shown how these speciications are used to calculate the Hausdorr dimension and Hausdorr measure of such sets. Since the appearence of Mandelbrot's 11 book \Fractals, Form, Chance and Dimen-sion" Fractal Geometry as a means providing a theory describing many of ...

Today, industrial production lines commonly use off-line and automatic on-line quality monitoring and control. Monitoring and control units analyse data from a production process, and analysis should be able to obtain reliable information that correspond with the character of the data obtained. The character of the data set obtained from production processes or from products can be highly struc...

Estimating uncertain state variables of a general complex dynamical network with randomly incomplete measurements of transmitted output variables is investigated in this paper. The incomplete measurements, occurring randomly through the transmission of output variables, always cause the failure of the state estimation process. Different from the existing methods, we propose a novel method to ha...

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We consider heat kernels on different spaces such as Riemannian manifolds, graphs, and abstract metric measure spaces including fractals. The talk is an overview of the relationships between the heat kernel upper and lower bounds and the geometric properties of the underlying space. As an application some estimate of higher eigenvalues of the Dirichlet problem is considered.