Figure 5 | Scientific Reports

Figure 5

From: Integer-dimensional fractals of nonlinear dynamics, control mechanisms, and physical implications

Figure 5

Self-similarity of nonlinear dynamics and control mechanisms. SD(2) denotes the standard deviation of the similarity ratio sequence with size two as a measure of self-similarity level. A near zero SD(2) reflects high level of self-similarity. (a,b) The traces of SD(2) versus the stability coefficient γ for the NLARI’ stochastic stable fixed point, period cycles, and chaos when the amplitude indicator η2 is decreased by decreasing the disturbance standard deviation σ with the restorative delays of κ2 = 1 and κ2 = 4, respectively. (c,d) The traces of SD(2) of the deterministic stable fixed point, period cycles, and chaos for the NLARI in (a,b) without noise for κ2 = 1 and κ2 = 4, respectively. (e,f) The traces of SD(2) versus the stability coefficient γ for the NLARI’ stochastic stable fixed point, period cycles, and chaos when the amplitude indicator η2 is decreased by increasing the restoration coefficient β for κ2 = 1 and κ2 = 4, respectively. (g,h) The traces of SD(2) of the deterministic stable fixed point, period cycles, and chaos for the NLARI in (e,f) without noise for κ2 = 1 and κ2 = 4, respectively. In (ad), the resistance coefficient α = 1.1 and β (0.036, 5.76). In (eh), α (1, 2) and β (0.001, 0.04).

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