<p>State-dependent observation can alter the detectable signatures of regime change in stochastic nonlinear systems. We characterize observability collapse: a state-dependent loss of measurement sensitivity that can make observed variance decrease even while latent variance increases near bifurcation. The mechanism arises when the local sensitivity of the observation map vanishes near an attractor, so that the signal-bearing component of the observed variance is suppressed by the loss of local sensitivity in the measurement process. We formalize this effect for a supercritical pitchfork normal form under slow parameter drift and derive an analytical condition on the observation exponent that separates collapse from non-collapse regimes. Numerical simulations confirm the predicted behaviour: Under identical latent dynamics approaching bifurcation, a state-dependent observation with vanishing sensitivity produces declining observed variance, whereas a control observation with bounded sensitivity produces the expected variance increase. A three-way ablation isolates the observation function as the causal source of suppression, and a parameter sweep over observation exponent and noise level supports the predicted collapse boundary. These results recast loss of transition detectability as a joint property of nonlinear dynamics and observation, and provide a compact computational demonstration of a structural failure mode in stochastic nonlinear systems.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

State-dependent observation and detectability collapse in stochastic nonlinear systems

  • Aldo Alberto Aguilar Bermúdez

摘要

State-dependent observation can alter the detectable signatures of regime change in stochastic nonlinear systems. We characterize observability collapse: a state-dependent loss of measurement sensitivity that can make observed variance decrease even while latent variance increases near bifurcation. The mechanism arises when the local sensitivity of the observation map vanishes near an attractor, so that the signal-bearing component of the observed variance is suppressed by the loss of local sensitivity in the measurement process. We formalize this effect for a supercritical pitchfork normal form under slow parameter drift and derive an analytical condition on the observation exponent that separates collapse from non-collapse regimes. Numerical simulations confirm the predicted behaviour: Under identical latent dynamics approaching bifurcation, a state-dependent observation with vanishing sensitivity produces declining observed variance, whereas a control observation with bounded sensitivity produces the expected variance increase. A three-way ablation isolates the observation function as the causal source of suppression, and a parameter sweep over observation exponent and noise level supports the predicted collapse boundary. These results recast loss of transition detectability as a joint property of nonlinear dynamics and observation, and provide a compact computational demonstration of a structural failure mode in stochastic nonlinear systems.