在复杂网络中，一个常见的数据挖掘任务是确定单个节点对系统行为的贡献。现有方法依赖于静态图中心性或控制理论量（如可控性格拉米安），后者假设系统具有线性、时不变动力学。然而，实际估计的系统通常是非线性和时变的。我们定义了“涌现贡献（Emergent Contribution, EC）”，这是一种有限时间范围内的节点动力学杠杆度量：即其脉冲响应沿系统轨迹累积的度量加权能量。EC 可从任意可微模型的雅可比矩阵计算得出，不依赖于具体估计器，并在系统为线性、时不变的极限情形下严格退化为平均可控性。本文贡献在于刻画了 EC 与平均可控性二者一致与分歧的条件。我们利用一个具有已知真实贡献的受控合成系统族，构建了一个涵盖非线性程度、相态结构、持续性及扰动幅度的相图。结果表明，在静态或平滑漂移的动力学下，EC 与平均可控性一致，且二者均能跟踪真实贡献；而在持续相态切换下出现分歧，在持续符号翻转下分歧最强，当符号翻转被移除时分歧消失；在极端扰动幅度下，两种度量均退化，从而揭示了局部线性化的适用边界。我们将来自多个领域的五个实证估计系统置于该相空间中，其位置可作为诊断依据，用以判断 EC 是否提供了超越静态可控性的额外信息，进而证明其额外计算成本的合理性。在一项深入分析的案例中，由二十次种子重训练构成的集成揭示了一种稳健的方差–杠杆解耦现象：某些节点的扰动虽在系统内部方差较低，却能广泛传播，而这一现象无法被

A recurring data mining task in complex networks is to determine how individual nodes contribute to system behavior. Existing approaches rely on either static-graph centralities or control-theoretic quantities such as controllability Gramians, which assume linear, time-invariant dynamics. Estimated systems, however, are typically nonlinear and time-varying. We define "emergent contribution (EC)," a finite-horizon measure of a node's dynamical leverage: the metric-weighted energy of its impulse response accumulated along the system trajectory. Computed from the Jacobians of any differentiable model, EC is estimator-agnostic and reduces exactly to average controllability in the linear, time-invariant limit. Our contribution is a characterization of when the two measures agree and diverge. Using a controlled synthetic family with known ground-truth contribution, we construct a phase diagram spanning nonlinearity, regime structure, persistence, and perturbation amplitude. EC and average controllability agree under static or smoothly drifting dynamics and both track ground truth. Divergence emerges under persistent regime switching, is strongest under persistent sign reversal, and disappears when the sign reversal is removed. At extreme perturbation amplitudes, both measures degrade, identifying the limits of local linearization. We place five estimated real systems from several domains within this phase space. Their placement serves as a diagnostic of when EC provides information beyond static controllability and therefore justifies its additional computational cost. On one panel examined in depth, a twenty-seed retraining ensemble reveals a robust variance--leverage dissociation: nodes whose perturbations propagate widely despite low within-system variance, which is not recovered by static centralities nor variance-based summaries.