Typical Perturbations Research Articles

Robust control of uncertain fully actuated systems with nonlinear uncertainties and perturbed input matrices

Robust control of uncertain fully actuated systems (FASs) with nonlinear uncertainties and perturbed input matrices is considered. Motivated by the recent work on this issue, two novel robust controllers are further developed for two cases under different assumptions. For both cases, the assumption on the perturbation input matrix in the previous work is relaxed to a significant extent, which allows many typical perturbation input matrices, such as constant ones, to be handled, while the previous method cannot. Moreover, for the first case, the assumption on the system uncertainty is further relaxed, and the states of the closed-loop system are globally bounded and converge into an arbitrarily small spherical domain centered at the origin. For the second case, with another requirement on the system nonlinearity imposed, the global exponential stability of the closed-loop system is achieved. The successful application in an electromechanical system verifies the effectiveness of the method.

An Innovative Approach in Inspecting a Damped Mathieu Cubic–Quintic Duffing Oscillator

Abstract Purpose The objective of the present study is to analyze a damped Mathieu–cubic quintic Duffing oscillator as a parametric nonlinear oscillatory dynamical system. This equation has multiple applications in diverse fields, including optics, quantum physics, and general relativity. There are multiple concerns related to periodic motion and the analysis of boundary-value problems with elliptic symmetries. The current effort aims to determine the frequency amplitude of parametric nonlinear issues. Method The non-perturbative approach (NPA) is employed to transform the nonlinear ordinary differential equation (ODE) into a linear equation. The derivation of the approximate solutions is achieved without relying on typical perturbation approaches, separate from the series expansion. Hence, the objective of this study is to depart from traditional perturbation methods and acquire approximated solutions for minor amplitude parametric components without imposing any limitations. Furthermore, the technique is extended to ascertain optimal solutions for the nonlinear large amplitude of fluctuation. Results The current approach allows for rapid estimation of the frequency-amplitude relationship in order to attain successive approximations of the solutions for parametric nonlinear fluctuations. A validation is obtained for the derived parametric equation, demonstrating a high level of agreement with the original equation. An analysis of stability behavior is conducted in multiple scenarios. In addition, the Floquet theory is used to examine the transition curves. Conclusion The current technique is characterized by its clear principles, making it practical, user-friendly, and capable of achieving exceptionally high numerical precision. The current approach is highly beneficial for addressing nonlinear parametric problems due to its ability to minimize algebraic complexity during implementation.

Linear response due to singularities

It is well known that a family of tent-like maps with bounded derivatives has no linear response for typical deterministic perturbations changing the value of the turning point. In this note we prove the following result: if we consider a tent-like family with a cusp at the turning point, we recover the linear response. More precisely, let T ɛ be a family of such cusp maps generated by changing the value of the turning point of T 0 by a deterministic perturbation and let h ɛ be the corresponding invariant density. We prove that ε↦hε is differentiable in L 1 and provide a formula for its derivative.

Driver-response relationships in a large shallow lake since the Anthropocene: Short-term abrupt perturbations versus long-term sustainable.

Lakes, as integral social-ecological systems, are hotspots for exploring climatic and anthropogenic impacts, with crucial pathways revealed by continuous sediment records. However, the response of multi-proxies in large shallow lakes to typical abrupt events and sustained drivers since the Anthropocene remains unclear. Here, we explored the driver-identification relationships between multi-proxy peaks and natural and anthropogenic events as well as the attribution of short-term perturbations and long-term pressures. To this end, sediment core records, socio-ecological data, and documented events from official records were integrated into a large shallow lake (Dongting Lake, China). Significant causal cascades and path effects (goodness-of-fit: 0.488; total effect: -1.10; p < .001) were observed among catchment environmental proxies, lake biogenic proxies, and mixed-source proxies. The peak-event identification rate (PEIR) and event-peak driving rate were proposed, and values of 28.57%-46.43% and 50%-81.25% were obtained, respectively. The incomplete accuracy of depicting event perturbations using sediment proxies was caused by various information filters both inside and outside the lake. PEIRs for compound events were 1.41 (±0.72) and 1.09 (±0.46) times greater than those for anthropogenic-dominated and natural-dominated events, respectively. Furthermore, socio-economic activity, hydrologic dynamics, land-use changes, and agriculture exerted significant and persistent pressures, cumulatively contributing 55.3%-80.9% to alterations in sediment proxies. Relatively synergistic or antagonistic trends in temporal contributions of these forces were observed after 2000, which were primarily attributed to the "Grain for Green" project and the Three Gorges Dam. This study represents one of the few investigations to distinguish the driver-response relationship of multiple proxies in large shallow lakes under typical event perturbations and long-term sustained pressures since the Anthropocene. The findings will help policymakers and managers address ecological perturbations triggered by climate change and human activities over long-term periods.

Simplified Reactor Model for Microreactor Coupled with Helium Closed Brayton Cycle

Microreactors comprise a new actively developing class of very small advanced reactors that have the potential to be an alternative to carbon-intensive energy technologies. A microreactor based on high-temperature gas reactor (HTGR) technology is a very promising advanced reactor with inherent safety, and it can couple with a closed Brayton cycle for higher efficiency. Since dynamics characteristics are fundamental to analyzing a power generation system and a reactor is the main source of the dynamics characteristics of a system, it is necessary to study a microreactor model suitable for system analysis. The main goal is to simulate the performance of the previously mentioned integrated system, focusing on the details of the power conversion unit while still ensuring acceptable calculation times. Hence, a simplified reactor model is needed that could supply sufficiently accurate values of pressure drop and heat transfer across the core. In this paper, by simplifying the physical processes in a microreactor, a dynamic model described by differential algebraic equations is obtained based on the lumped parameter modeling methodology and the basic conservation of fluid mass, momentum, and energy. Coupling thermal hydraulics with neutron kinetics, the temperature coefficient of reactivity and xenon poisoning are considered. Finally, the model is programmed and calculated using Modelica language. The transient responses of the main parameters under typical perturbations are analyzed, and the results show that the responses are correct. Because of the effect of reactivity feedback, fluctuations of the main parameters caused by microperturbations eventually tend to stabilize. In addition, the effects of negative reactivity introduced by xenon poisoning under two typical dynamic processes are analyzed. In power regulation, excess reactivity is required to compensate for the negative reactivity introduced by 135Xe. The model and results can properly predict the systematic parameters and serve as a basis for system analysis of microreactor coupling with the helium closed Brayton cycle.

Effect of high-frequency jet velocity perturbations on impinging jets atomization characteristics

The atomization characteristics of impinging jets with high-frequency jet velocity perturbations is studied numerically based on the volume of fluid method. Three typical perturbation modes are considered to mimic the velocity discrepancies of jet flow in real engine conditions. Both the perturbation amplitude and frequency are investigated independently. Results show that the liquid sheet structure and atomization characteristics are significantly changed under the intrinsic perturbation frequency. The spectrum analysis is performed to reveal the specific phenomenon and explore the mechanism of different velocity perturbation modes. The analyses show that the atomization process is sensitive to perturbation frequency but its effectiveness diminishes significantly at excessively high frequencies. Additionally, when the frequency of velocity perturbation approaches the natural intrinsic frequency of sheet waves, resonance occurs within the liquid sheet for certain perturbation mode, leading to dramatic varies in breakup length and spray angle because the velocity superposition of the intrinsic and perturbed flow and its dynamics.

Hybridization of solitons in realistic non-instantaneous fibers

Non-local nonlinearities are an integral part of numerous physical systems. Yet, their dissipative nature makes it hard to identify and verify stable eigenstates rigorously. This work sheds new light onto the existence of temporally non-local solitons – a class of dissipative self-maintaining states in time theoretically predicted to emerge in media with a time-delayed (i.e., non-instantaneous) nonlinear response. Revisiting the non-instantaneous nonlinear Schrödinger equation introduced by Conti et al., I introduce a semi-analytical approach to reveal such non-instantaneous solitons in liquid-type media which exhibit realistic non-exponential response functions featuring both rise and decay times. I investigate the susceptibility of such states to typical perturbations, such as third-order dispersion, instantaneous Kerr nonlinearity, and causality of the material response. Empirical numeric experiments illustrate how non-instantaneous solitons may compete against and even fuse with instantaneous (Kerr-type) solitons to an inseparable hybrid solitary waves. While finding a numerical solution to define the nature of this mixed state remains a challenge, I introduce a phase balance condition and other benchmarks which will allow to identify the occurrence of such states in realistic liquid-core fiber systems in future work. The findings of this study give reason to hypothetize a new type of dissipative solitary state and provide new means to understanding information transport and system dynamics of highly non-instantaneous nonlinear systems, particularly liquid-core optical fibers and waveguides.

Typical perturbation theory: Conditions, accuracy, and comparison with a mesoscopic case.

The perturbation theory based on typicality introduced by Dabelow and Reimann [Phys. Rev. Lett. 124, 120602 (2020)0031-900710.1103/PhysRevLett.124.120602] and further refined by Dabelow etal. [Phys. Rev. Res. 2, 033210 (2020)2643-156410.1103/PhysRevResearch.2.033210; J. Stat. Mech. (2021) 0131061742-546810.1088/1742-5468/abd026] provides a powerful tool since it is intended to be applicable to a wide range of scenarios while relying on only a few parameters. Even though the authors present various examples to demonstrate the effectiveness of the theory, the conditions used in its derivation are often not thoroughly checked. It is argued that this is justified (without analytical reasoning) by the robustness of the theory. In the paper at hand, said perturbation theory is tested on three spin-based models. The following criteria are taken into focus: the fulfillment of the conditions, the accuracy of the predicted dynamics, and the relevance of the results with respect to a mesoscopic case.

Impacts of filler loading and particle size on the transition to linear-nonlinear dichotomy in the rheological responses of particle-filled polymer solutions

In this study, the nonlinear behavior of carbon black-filled polybutadiene solutions under large-amplitude oscillatory shear is investigated. The results show that in the nonlinear regime, the third harmonic intensity, as measured by the ratio of the third to the first harmonics I3/I1, decreases significantly above a critical concentration ϕc of the polymer in the matrix, which results in the amplitude stress deviating strongly from the linear dependence of strain, while the time dependence of stress remains sinusoidal. Increasing the filler particle size significantly decreases the critical ϕc. However, increasing the filler loading basically has no effect on the transition to linear-nonlinear dichotomy. This transition happens when the mesh size ξ of the entangled polymer network in the matrix becomes smaller than the primary filler particle size. Above ϕc, the topological hindrance of the entangled polymer chains apparently considerably slows down the recovery speed of the broken filler network in the material. Hence, the quasisinusoidal response in the system that has a strain-dependent modulus is probably due to the restoration of the broken filler network requiring longer than the time scale of a typical dynamic perturbation.

Evaluation of Trigeminocardiac Reflex in Patients Undergoing Elevation of Zygomatic Fractures

AimTrigeminocardiac reflex (TCR) manifests as typical hemodynamic perturbations including a sudden lowering of heart rate, mean arterial blood pressure (MABP), cardiac arrhythmias, and asystole. In literature, TCR has been seen during ocular surgeries, Lefort fractures, and craniofacial surgeries. However, the prevalence of the TCR has not been studied in zygomatic complex fractures . The aim of this study was to assess the prevalence of TCR in patients undergoing elevation with/without fixation of zygomatic complex fractures and isolated zygomatic arch fractures under local anesthesia and general anesthesia and to evaluate the prevalence of TCR in different age groups.Materials and methodsThe study comprised 26 participants diagnosed with zygomatic fractures indicated for surgical intervention. The aim of the study was to find the prevalence of TCR in patients undergoing surgical intervention (elevation of zygomatic complex fractures with/without fixation) under local anesthesia and general anesthesia. The heart rate and blood pressure were measured preoperatively, intraoperatively and postoperatively.ResultsVariation in heart rate was seen in patients undergoing surgery under local anesthesia and general anesthesia. However, a decrease in the heart rate i.e., bradycardia was noted intra-operatively in 75% of the patients operated under local anesthesia. The prevalence of TCR was noted intra-operatively in 23% of cases operated under general anesthesia. No significant changes were seen in the blood pressure of the patients.ConclusionIn our study, we found out that the prevalence of TCR was more in the patients operated under local anesthesia i.e., 75% of patients. Out of the patients operated under general anesthesia i.e., 23% of patients showed TCR. No significant variations in blood pressure were observed in patients operated under local anesthesia or general anesthesia. The prevalence of TCR was found more often in the age group of 31-45 years in our study.

Robust Finite-Time Control Algorithm Based on Dynamic Sliding Mode for Satellite Attitude Maneuver

Robust finite-time control algorithms for satellite attitude maneuvers are proposed in this paper. The standard sliding mode is modified, hence the inherent robustness could be maintained, and this fixed sliding mode is modified to dynamic, therefore the finite-time stability could be achieved. First, the finite -time sliding mode based on attitude quaternion is proposed and the loose finite-time stability is achieved by enlarging the sliding mode parameter. In order to get the strict finite-time stability, a sliding mode based on the Euler axis is then given. The fixed norm property of the Euler axis is used, and a sliding mode parameter without singularity issue is achieved. System performance near the equilibrium point is largely improved by the proposed sliding modes. The singularity issue of finite-time control is solved by the property of rotation around a fixed axis. System finite-time stability and robustness are analyzed by the Lyapunov method. The superiority of proposed controllers and system robustness to some typical perturbations such as disturbance torque, model uncertainty and actuator error are demonstrated by simulation results.

Unravelling protein turnover in Duchenne muscular dystrophy: one protein at a time.

Unravelling protein turnover in Duchenne muscular dystrophy: one protein at a time.

Intermittency acceleration of water droplet population dynamics inside the interfacial layer between cloudy and clear air environments

The formation and life-span of clouds as well as the associated unsteady processes concerning the micro-physics of the water phases they may contain are open questions in atmospheric physics.We here use three-dimensional direct numerical simulation to analyse the temporal evolution of a small portion of the top of a cloud. The Eulerian description of the turbulent velocity, temperature and vapor fields is combined with the Lagrangian description of two different ensembles of cloud droplets, that is, with a monodisperse and a polydisperse size distribution. A shear-free turbulent mixing layer is used to model the background air flow of the cloud top. This flow is considered appropriate because clouds cannot stand the presence of shear, which inevitably destroys them quickly. Luke-warm clouds are generally found at an altitude of 1000-2000 meters, live for a few hours or up to 1-2 days, continuously change shape, and have typical dimensions of some hundreds of meters. The global time-scale of these changes is recognized as being of the order of 100 seconds (Shaw (2003), Warhaft (2009)). From the formation phase to the dying out phase, clouds live under a continuous sequence of transients that are slightly different one from the other.In this study, we have tried to reduce the simplification level with respect to the real warm cloud situation as much as possible. We have included the same level of supersaturation of warm clouds, the same amount of liquid water content, and thus, the same numerical number of water droplets, and finally, a typical unstable perturbation of the density stratification and a typical kinetic energy cloud / clear air ratio (order of 10). We have considered an observation duration of the order of a few seconds (about 10 initial turnaround times). During this time, the kinetic energy decays throughout the system by 95%. It should be recalled that the kinetic energy inside the interfacial layer (the shear-free turbulent mixing layer that matches the cloud region to the ambient air region) also decays spatially, by nearly 85%. We observed, with respect to the cloud region, in the interfacial layer, a five times faster achievement of a common value of standard deviation for the probability density of both the monodisperse and poly-disperse populations. This acceleration of the dynamics is remarkable and is somewhat counterintuitive. It is closely correlated with the intermittency of the small scale of the air flow and of the supersaturation fluctuation. We give information on the size distribution of both the positive and negative droplet growth and on the drop size and the corresponding numerical concentration value of the distribution peak as time passes. Finally, we comment on the extension of the concept of the collision kernel for an unstable and inhomogeneous system in which turbulence decays faster than the time scales of the involved aqueous phases.

Untargeted metabolomics as an unbiased approach to the diagnosis of inborn errors of metabolism of the non-oxidative branch of the pentose phosphate pathway

Inborn errors of metabolism (IEM) involving the non-oxidative pentose phosphate pathway (PPP) include the two relatively rare conditions, transketolase deficiency and transaldolase deficiency, both of which can be difficult to diagnosis given their non-specific clinical presentations. Current biochemical testing approaches require an index of suspicion to consider targeted urine polyol testing. To determine whether a broad-spectrum biochemical test could accurately identify a specific metabolic pattern defining IEMs of the non-oxidative PPP, we employed the use of clinical metabolomic profiling as an unbiased novel approach to diagnosis.Subjects with molecularly confirmed IEMs of the PPP were included in this study. Targeted quantitative analysis of polyols in urine and plasma samples was accomplished with chromatography and mass spectrometry. Semi-quantitative unbiased metabolomic analysis of urine and plasma samples was achieved by assessing small molecules via liquid chromatography and high-resolution mass spectrometry. Results from untargeted and targeted analyses were then compared and analyzed for diagnostic acuity.Two siblings with transketolase (TKT) deficiency and three unrelated individuals with transaldolase (TALDO) deficiency were identified for inclusion in the study. For both IEMs, targeted polyol testing and untargeted metabolomic testing on urine and/or plasma samples identified typical perturbations of the respective disorder. Additionally, untargeted metabolomic testing revealed elevations in other PPP metabolites not typically measured with targeted polyol testing, including ribonate, ribose, and erythronate for TKT deficiency and ribonate, erythronate, and sedoheptulose 7-phosphate in TALDO deficiency. Non-PPP alternations were also noted involving tryptophan, purine, and pyrimidine metabolism for both TKT and TALDO deficient patients.Targeted polyol testing and untargeted metabolomic testing methods were both able to identify specific biochemical patterns indicative of TKT and TALDO deficiency in both plasma and urine samples. In addition, untargeted metabolomics was able to identify novel biomarkers, thereby expanding the current knowledge of both conditions and providing further insight into potential underlying pathophysiological mechanisms. Furthermore, untargeted metabolomic testing offers the advantage of having a single effective biochemical screening test for identification of rare IEMs, like TKT and TALDO deficiencies, that may otherwise go undiagnosed due to their generally non-specific clinical presentations.

Radiomics for glioblastoma survival analysis in pre-operative MRI: exploring feature robustness, class boundaries, and machine learning techniques

BackgroundThis study aims to identify robust radiomic features for Magnetic Resonance Imaging (MRI), assess feature selection and machine learning methods for overall survival classification of Glioblastoma multiforme patients, and to robustify models trained on single-center data when applied to multi-center data.MethodsTumor regions were automatically segmented on MRI data, and 8327 radiomic features extracted from these regions. Single-center data was perturbed to assess radiomic feature robustness, with over 16 million tests of typical perturbations. Robust features were selected based on the Intraclass Correlation Coefficient to measure agreement across perturbations. Feature selectors and machine learning methods were compared to classify overall survival. Models trained on single-center data (63 patients) were tested on multi-center data (76 patients). Priors using feature robustness and clinical knowledge were evaluated.ResultsWe observed a very large performance drop when applying models trained on single-center on unseen multi-center data, e.g. a decrease of the area under the receiver operating curve (AUC) of 0.56 for the overall survival classification boundary at 1 year. By using robust features alongside priors for two overall survival classes, the AUC drop could be reduced by 21.2%. In contrast, sensitivity was 12.19% lower when applying a prior.ConclusionsOur experiments show that it is possible to attain improved levels of robustness and accuracy when models need to be applied to unseen multi-center data. The performance on multi-center data of models trained on single-center data can be increased by using robust features and introducing prior knowledge. For successful model robustification, tailoring perturbations for robustness testing to the target dataset is key.

A probabilistic Takens theorem

Let be a Borel set, μ a Borel probability measure on X and T : X → X a locally Lipschitz and injective map. Fix strictly greater than the (Hausdorff) dimension of X and assume that the set of p-periodic points of T has dimension smaller than p for p = 1, …, k − 1. We prove that for a typical polynomial perturbation of a given locally Lipschitz function , the k-delay coordinate map is injective on a set of full μ-measure. This is a probabilistic version of the Takens delay embedding theorem as proven by Sauer, Yorke and Casdagli. We also provide a non-dynamical probabilistic embedding theorem of similar type, which strengthens a previous result by Alberti, Bölcskei, De Lellis, Koliander and Riegler. In both cases, the key improvements compared to the non-probabilistic counterparts are the reduction of the number of required coordinates from 2 dim X to dim X and using Hausdorff dimension instead of the box-counting one. We present examples showing how the use of the Hausdorff dimension improves the previously obtained results.

Nonlinear responses of carbon black-filled polymer solutions to forced oscillatory shear

Systematic rheometric measurements are carried out to explore the nonlinear responses of carbon black-filled polyisoprene/squalene solutions with the polymer concentrations ϕ in the matrix ranging from the coil overlapping state (ϕ =ϕ*) to the melt state (ϕ =1). At the coil overlapping state, when ϕ <<1, the system typically shows the classic nonlinearity, where the storage modulus G’ decreases as strain amplitude γ0 increases and the resulting stress responses are distorted and deviated from normal sinusoidal waves. At the melting state when ϕ = 1, the system displays a new nonlinearity, where the stress responses to forced oscillatory shear are surprisingly sinusoidal regardless the reduction of G’ as the strain amplitude is increased. Between the two states when ϕ*< ϕ <1, the system exhibits an anomalous and complex nonlinear rheological behavior throughout a wide range of polymer concentrations. The ratio of the third to the first harmonics (I3/I1) in the stress responses first decreases rapidly reaching a minimum when ϕ ≈ 0.1, then increases to a maximum when ϕ ≈ 0.3, after which it decreases again as ϕ approaches the melt state. Lowering the test frequency shifts horizontally the minimum and the maximum in I3/I1 vs ϕ to the right. Increasing strain amplitude intensifies this anomalous behavior. Remarkably, the restoration of broken filler network in the polymer/solvent media also displays the corresponding minimum and maximum values. The quasi-sinusoidal or linear dynamic response in a system that has a strain-dependent modulus is apparently due to the restoration of broken filler network requiring longer than the time scale of a typical dynamic perturbation.

Acoustic wave generation in collapsing massive stars with convective shells

ABSTRACT The convection that takes place in the innermost shells of massive stars plays an important role in the formation of core-collapse supernova explosions. Upon encountering the supernova shock, additional turbulence is generated, amplifying the explosion. In this work, we study how the convective perturbations evolve during the stellar collapse. Our main aim is to establish their physical properties right before they reach the supernova shock. To this end, we solve the linearized hydrodynamics equations perturbed on a stationary background flow. The latter is approximated by the spherical transonic Bondi accretion, while the convective perturbations are modelled as a combination of entropy and vorticity waves. We follow their evolution from large radii, where convective shells are initially located, down to small radii, where they are expected to encounter the accretion shock above the proto-neutron star. Considering typical vorticity perturbations with a Mach number ∼0.1 and entropy perturbations with magnitude ∼0.05kb/baryon, we find that the advection of these perturbations down to the shock generates acoustic waves with a relative amplitude $\delta {\rm p}/\gamma {\rm p} \lesssim 10{{\ \rm per\ cent}}$, in agreement with published numerical simulations. The velocity perturbations consist of contributions from acoustic and vorticity waves with values reaching ${\sim}10{{\ \rm per\ cent}}$ of the sound speed ahead of the shock. The perturbation amplitudes decrease with increasing ℓ and initial radii of the convective shells.

Temperature control strategy for polymer electrolyte fuel cells

A polymer electrolyte fuel cell (PEFC) is an electrochemical device that converts chemical energy directly to electrical energy, and its performance greatly depends on its operating temperature. Therefore, in this paper, a novel thermodynamic PEFC model with the airflow cooling method is firstly developed for the PEFC system. Then, a novel model predictive control (MPC) controller is designed to control the stack temperature at an optimal value by adjusting the air flow rate on the basis of the developed thermodynamic PEFC model. The thermodynamic PEFC model and the designed controlling strategies are simulated and analysed in Matlab/Simulink. Three tests are conducted to estimate the reliability of the developed controllers concerning different operating conditions: (a) typical perturbation in the current load, (b) any perturbation in the current load, and (c) variation of the ambient temperature. The simulation results demonstrate that the MPC controller can effectively control the stack temperature at the desired value. Moreover, the MPC controller shows much superior effects compared with the conventional proportional integral derivative (PID) controller. In addition, the developed coolant circuit model can be easily applied to various PEFC systems. The MPC controller shows potential also for other controlling issues of PEFC systems due to its strong robustness and fast response.

Robustness of Gaian feedbacks to climate perturbations

ABSTRACT The Gaia hypothesis postulates that life regulates its environment to be favorable for its own survival. Most planets experience numerous perturbations throughout their lifetimes such as asteroid impacts, volcanism, and the evolution of their host star’s luminosity. For the Gaia hypothesis to be viable, life must be able to keep the conditions of its host planet habitable, even in the face of these challenges. ExoGaia, a model created to investigate the Gaia hypothesis, has been previously used to demonstrate that a randomly mutating biosphere is in some cases capable of maintaining planetary habitability. However, those model scenarios assumed that all non-biological planetary parameters were static, neglecting the inevitable perturbations that real planets would experience. To see how life responds to climate perturbations to its host planet, we created three climate perturbations in ExoGaia: one rapid cooling of a planet and two heating events, one rapid and one gradual. The planets on which Gaian feedbacks emerge without climate perturbations are the same planets on which life is most likely to survive each of our perturbation scenarios. Biospheres experiencing gradual changes to the environment are able to survive changes of larger magnitude than those experiencing rapid perturbations, and the magnitude of change matters more than the sign. These findings suggest that if the Gaia hypothesis is correct, then typical perturbations that a planet would experience may be unlikely to disrupt Gaian systems.