## Biophysics

**Complex Systems**

**Non-linear functions determine biology**

Every feedback as a prerequisite for biochemical metabolic control leads to a quadratic term of the corresponding function and thus represents a non-linear function. This is the basis of the deterministic chaotic time series.

The interpretationj of the empirically determined time series requires the methods of complex systems.

**Fractal dimensions determine our world**

There is no straight line (D=1), plane surface (D=2) or purely three-dimensional spatial form (D=3) in nature. We find so-called fractal dimensions (D= 1.7; 2.4; 3.6; but also D= 7.3).

The fractal dimension is an expression of the complexity of a function and can be determined empirically. This can be used in the double logarithmic plot to represent changes in complexity (e.g. disease) or to recognise them in the first place.

**Biological stability is defined by the attractor**

Regardless of the type and extent of deflection, the pendulum always returns to the lowest point of the oscillation path due to gravity (point attractor). Similarly, “biologically stable” (steady state, etc.) systems find a state that can be represented as the typical state space of the system, e.g. developed from an empirical time series in the reversal plot (phase portrait). Systems without attractors are not found in the evolution of organisms or in developmental biology.

**Methodical applications in medicine**

From glycolysis oscillation, changes in heart rate or osteoporosis to changes in alpha waves in the electroencephalogram of the brain during epileptic seizures, the methods of complex systems have gained practical relevance.

Similarly, without knowledge of complex systems, it is impossible to understand the development of chronic diseases or to develop a suitable causal therapy