Figure 1

The phase trajectories in the $x\text{−}z$ plane are recorded for different $ϵ$ from (a) to (e). Top panels are for the oscillator 1 and the bottom for the oscillator 2.Reuse & Permissions

Figure 2

The time evolutions of the variable $x$ are recorded for different $ϵ$ from (a) to (e). (f) The time evolution of the variable $z$ with the same $ϵ$ as (e). Top panels are for the oscillator 1 and the bottom for the oscillator 2.Reuse & Permissions

Figure 3

(Color online) (a) and (b) The bifurcation diagrams versus $ϵ$ for $x_1$ and $x_2$, respectively. The data is obtained when $x_1$ reaches its maximum. (c) The first three largest Lyapunov exponents, $\Lambda$, are plotted versus $ϵ$. The insets in (a), (b), and (c) enlarge the narrow parameter region for $ϵ∊(6,6.05)$ where the partial amplitude death loses its stability.Reuse & Permissions

Figure 4

$ϵ=5.95$ is close to the crisis-induced transition. (a) and (b) The evolutions of $x\left(1\right)$ and $x\left(2\right)$ where the intermittency is clear. (c) A time period of the evolution of $x\left(1\right)$ and $x_2$ is shown where one exchange between the states of the oscillators occurs. (d) The trajectory of $x_2$ in $x\text{−}z$ plane during the time period in (c) where we can find that the large amplitude oscillation jumps to another wing of the Lorenz attractor.Reuse & Permissions

Figure 5

(a) The time series of the instantaneous maximum growth rate $\Lambda$ (bold curve) and $z_2$. $ϵ=6.05$. (b) The Lyapunov exponents versus $ϵ$ are plotted for the subsystem of $x_2$ and $y_2$. The onset of the instability of the partial amplitude death is a little larger than $ϵ=6$.Reuse & Permissions

Figure 6

The phase diagram for the partial amplitude death. (a) $\sigma =10.19$ and $b=2.664$. (b) $r=28.17$ and $b=2.664$.Reuse & Permissions