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Nicotine is unusual in comparison to most drugs, as its profile changes from stimulant to sedative with increasing dosages, a phenomenon known as "Nesbitt's paradox" after the doctor who first described it in 1969. [135] [136] At very high doses it dampens neuronal activity. [137] Nicotine induces both behavioral stimulation and anxiety in ...
Mackey–Glass attractors for various values of the parameter . It is of interest to study the behaviour of the equation solutions when is varied, since it represents the time taken by the physiological system to react to the concentration variation of a substance.
The Poincaré recurrence time is the length of time elapsed until the recurrence. This time may vary greatly depending on the exact initial state and required degree of closeness. The result applies to isolated mechanical systems subject to some constraints, e.g., all particles must be bound to a finite volume.
Informally, dynamical systems describe the time evolution of the phase space of some mechanical system. Commonly, such evolution is given by some differential equations, or quite often in terms of discrete time steps.
The equations are a set of differential equations – over time – of the probabilities that the system occupies each of the different states. The name was proposed in 1940: [ 1 ] [ 2 ] When the probabilities of the elementary processes are known, one can write down a continuity equation for W, from which all other equations can be derived and ...
Relaxation methods are used to solve the linear equations resulting from a discretization of the differential equation, for example by finite differences. [ 2 ] [ 3 ] [ 4 ] Iterative relaxation of solutions is commonly dubbed smoothing because with certain equations, such as Laplace's equation , it resembles repeated application of a local ...
Linear Time Invariant (LTI) Systems are those systems in which the parameters , , and are invariant with respect to time. One can observe if the LTI system is or is not controllable simply by looking at the pair ( A , B ) {\displaystyle ({\boldsymbol {A}},{\boldsymbol {B}})} .
The Crank–Nicolson stencil for a 1D problem. The Crank–Nicolson method is based on the trapezoidal rule, giving second-order convergence in time.For linear equations, the trapezoidal rule is equivalent to the implicit midpoint method [citation needed] —the simplest example of a Gauss–Legendre implicit Runge–Kutta method—which also has the property of being a geometric integrator.
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