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Despite the great potential complexity and diversity of biological networks, all first-order network behavior generalizes to one of four possible input-output motifs: hyperbolic or Michaelis–Menten, ultra-sensitive, bistable, and bistable irreversible (a bistability where negative and therefore biologically impossible input is needed to return from a state of high output).
This leads to a simple first-order differential equation which describes heat transfer in these systems. Having a Biot number smaller than 0.1 labels a substance as "thermally thin," and temperature can be assumed to be constant throughout the material's volume.
The bilinear transform is a first-order approximation of the natural logarithm function that is an exact mapping of the z-plane to the s-plane. When the Laplace transform is performed on a discrete-time signal (with each element of the discrete-time sequence attached to a correspondingly delayed unit impulse), the result is precisely the Z ...
Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...
The transfer function of a two-port electronic circuit, such as an amplifier, might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical actuator might be the mechanical displacement of the movable arm as a function of electric ...
Biological thermodynamics (Thermodynamics of biological systems) is a science that explains the nature and general laws of thermodynamic processes occurring in living organisms as nonequilibrium thermodynamic systems that convert the energy of the Sun and food into other types of energy.
Hence the equation expresses that the rate of change of the predator's population depends upon the rate at which it consumes prey, minus its intrinsic death rate. The Lotka–Volterra predator-prey model makes a number of assumptions about the environment and biology of the predator and prey populations: [5]
By applying a Laplace transform to the LTI system above, the transfer function becomes = () = = =For general orders and this is a non-rational transfer function. Non-rational transfer functions cannot be written as an expansion in a finite number of terms (e.g., a binomial expansion would have an infinite number of terms) and in this sense fractional orders systems can be said to have the ...