Cross-validation test applied to coupled limit cycle predator-prey model. For order number , error function is computed for the test data, which are not used for the parameter estimation. The minimum error points the optimum Fourier order at .
Interaction function of limit cycle predator-prey model is drawn for the first oscillator (solid line) and for the second oscillator (dotted line). (a) The estimates based upon the perturbation method and (b) estimates based upon the present method.
Synchronization diagram of two coupled limit cycle predator-prey model. Normalized mean frequency difference is plotted against the coupling strength . The model prediction (dotted line) is compared with the simulation curve (solid line), which is drawn by using the original Eqs. (6) and (7) . The circle marker corresponds to the coupling strength utilized for the model estimation.
Dependence of the prediction error of the synchronization diagram on the parameters and . (a) , , . (b) , , .
Dependence of the prediction error on (a) observational noise (from 0% to 25%) and (b) coupling strength used for generating the time series. The parameters are set to .
Chaotic attractor in -coordinate space of the predator-prey system (12)–(14) .
Dependence of the normalized frequency difference between the coupled predator-prey systems on the coupling strength . The coupling asymmetry is set as .
Synchronization diagrams are drawn for two coupled predator-prey system (solid line) and its nonlinear model (dotted line). Normalized frequency difference is plotted by changing the coupling strength . Locations of the data used for the modeling are indicated by the cross marks. (a) , (b) , (c) , (d) with 20% observational noise, and (e) with 30% observational noise.
Synchronization diagram of two diffusively coupled nonidentical Chua circuits. Frequency difference between the two circuits is plotted against coupling strength .
Synchronization diagram of the experimental system (solid line) and the model prediction (dotted line). Locations of the data used for the modeling are indicated by the crosses. (a) Data from , . (b) Data from , . (c) Data from , .
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