TY - JOUR
T1 - A structural approach to control of transitional waves of nonlinear diffusion-reaction systems
T2 - Theory and possible applications to bio-medicine
AU - Kardashov, Victor
AU - Einav, Shmuel
PY - 2002
Y1 - 2002
N2 - This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion). The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients). The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions).
AB - This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion). The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients). The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions).
KW - Density dependent diffusion
KW - Finite localized transients
KW - Pulse propagations chaos degree
KW - Structural interaction
UR - http://www.scopus.com/inward/record.url?scp=17944368480&partnerID=8YFLogxK
U2 - 10.1080/10260220290013499
DO - 10.1080/10260220290013499
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AN - SCOPUS:17944368480
SN - 1026-0226
VL - 7
SP - 27
EP - 40
JO - Discrete Dynamics in Nature and Society
JF - Discrete Dynamics in Nature and Society
IS - 1
ER -