Applications of Chaos and Fractal Theories in the Field of Electromagnetic Scattering - Intelligent Computing for Sustainable Energy and Environment - page 63

the Twersky's in the way of ignoring the multiple scattered waves between the
same scatterers. Statistical quantities were studied for wave propagating in a
fractal medium and equation of wave field was obtained. The results of range
dependence of the intensity of the backscattered radar signals showed agreement
with the numerical simulation. So the developed theory and interrelated model
are effective [28].
Furthermore, scattering components of targets in radar communication in-
clude creeping waves scattered by shadows of target edge, echoes reflected by
mirror surface scattered waves from discontinuous area, scattered waves from
derivative discontinuous area, scattered waves from accidented area and scat-
tering waves produced by reciprocity of different parts of the surface. The reci-
procity of these waves make the process of target scattering behave strongly
nonlinearly. Based on it, Ming Xian and Zhao-wen Zhuang et al applied chaos
and fractals into the studies of analysis and recognition of radar targets scatter-
ing signal. The Lyapunov exponents of five kinds of plane waves are calculated
and the chaos inherent of radar echos was proved. The multifractal dimensions
of these targets' scattering signal were further obtained, providing a reliable
warrant for target recognition[29].
4 Conclusions
As ecient tools for studies of nonlinear system, chaos and fractal theories have
been widely applied in the field of electromagnetic scattering. In researches of the
modeling of random surface, the development of FBM and Weierstrass function
have greatly improved the development of electromagnetic scattering. This paper
mainly discusses the application of chaos and fractal theories on EM scattering
from the random rough surface, the modeling of sea surface, the studies of the sea
clutter, the scatters synthesis, the scattering communication and so on. Among
these, chaos theory and the fractal theory integrate well with each other in
studies of sea clutters and scattering communication.
It is obvious that the FBM is unpredictable, so do the chaos. So the process
of chaos may also be used in surface modeling, especially for sea surface model-
ing. As attractors have fractal characteristic, it is natural for a surface formed
based on the chaos dynamic to be fractal. So it is necessary to test whether the
phenomenon of chaos scattering will show up in fractal scatters. Since the chaos
theory mainly refers to nonlinear dynamic systems and fractal theory mainly fo-
cuses on the irregular geometric objects with infinite subdivision and self-similar
structure, the combination of the these theories will have a promising future with
wider applications.
Acknowledgments. This work was financially supported by the National Nat-
ural Science Foundation of China (No.61178066) and Natural Science Foundation
of Heilongjiang (No.F201013).