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The Rössler attractor Rössler attractor as a stereogram with =, =, = The Rössler attractor (/ ˈ r ɒ s l ər /) is the attractor for the Rössler system, a system of three non-linear ordinary differential equations originally studied by Otto Rössler in the 1970s.
The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor. A fixed point of a function or transformation is a point that is mapped to itself by the function or ...
The frequency response of this oscillator describes the amplitude of steady state response of the equation (i.e. ()) at a given frequency of excitation . For a linear oscillator with β = 0 , {\displaystyle \beta =0,} the frequency response is also linear.
The Lorenz attractor is difficult to analyze, but the action of the differential equation on the attractor is described by a fairly simple geometric model. [24] Proving that this is indeed the case is the fourteenth problem on the list of Smale's problems. This problem was the first one to be resolved, by Warwick Tucker in 2002. [25]
The multipactor effect is a phenomenon in radio-frequency (RF) amplifier vacuum tubes and waveguides, where, under certain conditions, secondary electron emission in resonance with an alternating electromagnetic field leads to exponential electron multiplication, possibly damaging and even destroying the RF device.
Rössler attractor reconstructed by Takens' theorem, using different delay lengths. Orbits around the attractor have a period between 5.2 and 6.2. In the study of dynamical systems, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence of observations of the state of that system.
The critical attractor. An attractor is a term used to refer to a region that has the property of attracting surrounding orbits, and is the orbit that is eventually drawn into and continues. The attractive fixed points and periodic points mentioned above are also members of the attractor family.
Schuler tuning is a design principle for inertial navigation systems that accounts for the curvature of the Earth. An inertial navigation system, used in submarines, ships, aircraft, and other vehicles to keep track of position, determines directions with respect to three axes pointing "north", "east", and "down".