There have been many literatures about implementation of chaotic oscillators using FPGA like FPGA based multiscroll attractor discussed in [32-39], digital chaotic oscillators and its FPGA model [36, 40], FPGA based four-wing chaotic attractor
, and image cryptography with chaotic ciphers and its FPGA implementations and FPGA implemented memristor-based chaotic attractors
When initial conditions are set as (0.1, 0.1, 0, 0), the system in (1) produces four-wing chaotic attractors
, as shown in Figure 1.
It moves from period-1 limit cycle to double band chaotic attractors
going through single band chaotic attractors
and tiny windows of periodic attractors.
Caption: FIGURE 2: Forced van der Pol chaotic attractor
in continuous-time (CA) and Poincare map (CA-PM) for [omega] = 0.45, [eta] =1, and a = 0.988.
Caption: Figure 6: Chaotic attractor
of the circuit with the 4D hyperchaotic memristive circuit.
The largest Lyapunov exponent, the chaotic attractor
, and the time series are also given to confirm the chaotic characteristic of the system.
Here, the verification for the WPAC basin is presented because of the larger sample size of strong storms that will facilitate our subsequent analysis of the MPI limit and chaotic attractor
. Except for the Naval Global Environmental Model (NVGM), which possesses an initial intensity error as large as the 4-5-day errors, all other models display the most rapid intensity error growth during the first 48 h despite very different vortex initial conditions and numerical modeling systems.
2.6 Forming mechanism for the structure of new chaotic attractor
The bifurcation diagrams and Lyapunov exponents spectrums for every parameter have been discussed and the parameter interval range of limit cycle and chaotic attractor
of every parameter have also been calculated.
The key issue here is that the operation of a chaotic attractor
is described as systematically removing initial information and replacing it with new information, but what is the initial information?
 Vincent UE, Synchronization of Rikitake chaotic attractor
using active control, Phys Lett A, 343(2005), No.
For [c.sub.1] < c < [c.sub.cr] [approximately equal to] 24.74, there is also a chaotic attractor
. Depending on the initial state, the system will converge to one of the two stable steady states or it will behave chaotically indefinitely.