By Jan Walleczek
The becoming effect of nonlinear technology on biology and medication is essentially altering our view of residing organisms and illness procedures. This booklet introduces the appliance to biomedicine of a large variety of suggestions from nonlinear dynamics, equivalent to self-organization, complexity, coherence, stochastic resonance, fractals, and chaos. Written via top figures within the box, insurance info experimental and theoretical learn, in addition to the rising technological probabilities equivalent to nonlinear regulate ideas for treating pathological biodynamics, together with center arrhythmias and epilepsy. Self-Organized organic Dynamics and Nonlinear keep an eye on will allure the curiosity of pros and scholars from a variety of disciplines, together with physicists, chemists, biologists, sensory physiologists and scientific researchers akin to cardiologists, neurologists and biomedical engineers.
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Extra info for Self-organized biological dynamics & nonlinear control
Sample text
The small arrows in Figure 8a indicate the lines along which were taken. All diagrams within (i) and (ii) have the same scaling of the x-axis. Ten slow external periods are shown in (a) and (c); 10 fast external periods in (b); : 1000 for both oscillators. 5 Combined influence of static, periodic and noisy signals In physical, chemical and biological systems noise is always present. Besides the internal noise the external signal may exhibit an additional noisy component (from the environment or from neighboring subsystems).
The governing dynamics is assumed to be determined by only a few variables. Then all the other variables can be replaced by their steady-state values. By an adiabatic elimination procedure for all the fast (irrelevant) variables, only a few equations result, an example being Equations (11), when only the variables x and y are relevant. This procedure is the basis for the concept of self-organization and synergetics (Haken, 1978). , see Milton, Chapter 16, this volume). Subsequently, the methods and concepts of nonlinear dynamics have to be applied to the resulting equations.
In each column four different values of F or F are chosen, increasing (i) Double-well oscilF ,F : F ,F to F ,F 9 F ,F from from top to bottom. lator; (ii) Multi-limit-cycle Van der Pol oscillator. (a) F : 0,F increasing: typical typical behavior of fast behavior for a slow excitation; (b) F : 0,F increasing: excitation; (c) combined influence of slow and fast signal, F : F and F increasing, the series but F : F . The small arrows in Figure 8a indicate the lines along which were taken.