Propagating nature in chaotic systems

Intrinsic chaos and external noise in population dynamics

“…So λ = ln Z. When Z = p/q, where p and q are relative primes, function (4) produces multivalued firsts-return maps [20,21,22,23]. In this case, the information lacking is not given by K = λ, but is larger: one loses information not only in each iteration due to λ > 0.…”

“…Very recently [20,21,22,23] we have investigated explicit functions which can produce truly random numbers…”

“…In Section 3 we recall the definition and properties of the random sequences given in Ref. [20,21,22,23], and we compute the complexity for the random sequences and a particular random map. In Section 4 we discuss a nonlinear time-series model constructed from sheep population data and we compute the complexity for this model.…”

A mechanism for randomness

“…However, a more detailed discussion of the properties of these functions (including statistical tests) can be found in Ref. [12][13][14].…”

“…Recently, we have introduced explicit functions that produce truly random sequences [12][13][14]. For instance, let us define the function:…”