Rossler system

Description

Generates a 3-dimensional time series using the Rossler equations.

Usage

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  rossler(a = 0.2, b = 0.2, c = 5.7,
    start = c(-2, -10, 0.2), time = seq(0, 50, by = 0.01),
    do.plot = TRUE)

Arguments

start

A 3-dimensional numeric vector indicating the starting point for the time series. Default: c(-2, -10, 0.2).

a

The a parameter. Default:0.2.

b

The b parameter. Default: 0.2.

c

The c parameter. Default: 5.7.

time

The temporal interval at which the system will be generated. Default: time=seq(0,50,by = 0.01).

do.plot

Logical value. If TRUE (default value), a plot of the generated Lorenz system is shown.

Details

The Rossler system is a system of ordinary differential equations defined as:

dx/dt = -(y + z)

dy/dt = x + a*y

dz/dt = b + z*(x-c)

The default selection for the system parameters (a = 0.2, b = 0.2, c = 5.7) is known to produce a deterministic chaotic time series.

Value

A list with four vectors named time, x, y and z containing the time, the x-components, the y-components and the z-components of the Rossler system, respectively.

Note

Some initial values may lead to an unstable system that will tend to infinity.

Author(s)

Constantino A. Garcia

References

Strogatz, S.: Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering (Studies in Nonlinearity)

See Also

henon, logisticMap, rossler, ikedaMap, cliffordMap, sinaiMap, gaussMap

Examples

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## Not run: 
r.ts = rossler(time=seq(0,30,by = 0.01))

## End(Not run)