Nonlinear Interaction Effects Research Articles

Proactive green innovation and firm climate resilience: the nonlinear interaction effect of climate risk.

Based on empirical analysis of 113 climate disasters affecting 3563 listed firms across 31 provinces in China from 2010 to 2022, as documented in the Emergency Events Database (EM-DAT), this study employs event study and multiple regression to explore the impact of proactive green innovation on firm climate resilience. By categorizing proactive green innovation into process and product innovation and climate resilience into short-term and long-term resilience, a proactive green innovation-firm climate resilience 2 × 2 matrix is constructed to provide innovative insights. This study reveals that proactive green innovation enhances firm climate resilience. Specifically, proactive green process innovation both enhances short-term and long-term climate resilience, while proactive green product innovation only enhances long-term rather than short-term climate resilience. Furthermore, climate disaster has inverted U-shaped interaction effect on the relationship between proactive green innovation and short-term climate resilience and U-shaped interaction effect on the relationship between proactive green innovation and long-term climate resilience. Additionally, this study also investigates the heterogeneous mechanisms of proactive green innovation enhancing short-term and long-term climate resilience based on network embeddedness theory and legitimacy theory.

Numerical investigation of nonlinear soil-structure interaction effects on response of irregular RC buildings

Kathmandu, located in a high seismic zone, predominantly features irregular structures among its building stock. These structures are particularly susceptible to severe damage during seismic events, primarily due to torsional effects. Traditional seismic designs rely particularly on fixed-base conditions that underestimate forces and displacement primarily on soft soil conditions leading to irrational design practices. This study aims to quantify the seismic performance of buildings on various base conditions through fully nonlinear Soil-structure Interaction (SSI). The soil nonlinear behaviour was modelled using the Pressure-Independ-Multi-Yield (PIMY) material with an octahedral shear stress-strain backbone curve. Three distinct soil types were considered, and structures with irregular plan configurations were modelled using finite elements in both Opensees and STKO platforms. Structural performance was analyzed through nonlinear dynamic analysis, and outputs were evaluated based on seismic parameters. Comparing nonlinear SSI with linear SSI and fixed-base conditions revealed a significant increase in structural response, expressed in terms of displacement, drift ratio, and base shear. The magnitude of diaphragm rotation was found to be influenced by a combination of building torsional irregularity and SSI effects. It is suggested that the conventional practice of using the torsional irregularity ratio as a measure of torsional irregularity be revised and enhanced to better account for these influences. It has been quantified that torsional irregularity has a relatively lesser impact on displacements, drifts, and base shear compared to SSI. In all cases, fixed-base conditions consistently exhibited the minimum response. The study explored that linear SSI and fixed-base conditions tend to underestimate structural responses, while nonlinear SSI coupled with dynamic analysis provides a more accurate representation of realistic structural behaviour for seismic design particularly in soft soil cases.

Species Diversity and Habitat Fragmentation Per Se: The Influence of Local Extinctions and Species Clustering.

AbstractAnthropogenic fragmentation of habitat is considered to be a critical factor contributing to the decline of species. However, a general consensus on the degree to which habitat loss and what has been called "habitat fragmentation per se" contribute to the loss of species diversity has not yet emerged. For empirical and theoretical reasons the topic has recently attracted renewed attention, thus reviving the "single large or several small" (SLOSS) debate. To study the effect of fragmentation per se, we use a spatially explicit and continuous, competitively neutral simulation model with immigration from a regional pool. The model accounts for the influence of ecological drift and intrafragment species clustering (due to limited dispersal) on local (plot) and global (landscape) diversity. We find that fragmentation increases global diversity but decreases local diversity, prominently so if fragments become more isolated. Cluster formation is a key mechanism reducing local diversity. By adding external disturbance events that lead to the occasional extinction of entire communities in habitat fragments, we show that the combined effect of such extinctions and cluster formation can create nonlinear interactive effects of fragmentation and fragment isolation on diversity patterns. We conclude that while in most cases fragmentation will decrease local and increase landscape diversity, universal predictions concerning the SLOSS debate should be taken with care.

Effect of non-local near-resonant interactions of Rossby waves on formation of large-scale zonal flows in unforced two-dimensional turbulence on rotating sphere

This study investigates the effect of nonlinear interactions of Rossby waves on large-scale zonal flow formation in two-dimensional turbulence on a rotating sphere. The coefficients of nonlinear interactions are first calculated. Then, the non-local, near-resonant, and non-local near-resonant interactions are investigated in detail. The results show that the formation of large-scale westward circumpolar zonal flows is directly caused by non-local energy transfer due to the three-wave near-resonant interactions of Rossby waves.

Mechanical response of tunnels crossing active fault zones under normal or reverse faulting: A refined nonlinear analytical approximate solution

Tunnels crossing active fault zones will be severely damaged under normal or reverse faulting. The tunnel-stratum interaction is nonlinear, and the fault zone width significantly affects the tunnel response. Nevertheless, the existing analytical models neglect the effect of nonlinear tunnel-stratum interaction or fault zone width and adopt unrealistic assumptions. This work proposes a refined nonlinear solution, considering the nonlinear tunnel-stratum interaction and fault zone width, and some widely employed assumptions are removed. Specifically, a tunnel under normal or reverse faulting is simplified to an elastic beam acting on a nonlinear foundation, the nonlinear tunnel-stratum interaction is considered by setting a series of nonlinear axial and vertical springs, and the fault zone width is considered by reducing the spring stiffness. Additionally, the nonlinear axial force and geometrical nonlinearity terms are considered in the governing equations. The comparison results indicate that the results obtained from the proposed model agree well with those from model tests and numerical models and have a better accuracy than the existing analytical models. Finally, the effects of fault, stratum, and lining parameters on the response of tunnels crossing normal or reverse faults are discussed regarding stress distribution and failure scope.

A global model of intensity autocorrelation to determine laser pulse duration

We present a new global model of collinear autocorrelation based on second harmonic generation nonlinearity. The model is rigorously derived from the nonlinear coupled wave equation specific to the autocorrelation measurement configuration, without requiring a specific form of the incident pulse function. A rigorous solution of the nonlinear coupled wave equation is obtained in the time domain and expressed in a general analytical form. The global model fully accounts for the nonlinear interaction and propagation effects within nonlinear crystals, which are not captured by the classical local model. To assess the performance of the global model compared to the classic local model, we investigate the autocorrelation signals obtained from both models for different incident pulse waveforms and different full-widthes at half-maximum (FWHMs). When the incident pulse waveform is Lorentzian with an FWHM of 200 fs, the global model predicts an autocorrelation signal FWHM of 399.9 fs, while the classic local model predicts an FWHM of 331.4 fs. The difference between the two models is 68.6 fs, corresponding to an error of 17.2%. Similarly, for a sech-type incident pulse with an FWHM of 200 fs, the global model predicts an autocorrelation signal FWHM of 343.9 fs, while the local model predicts an FWHM of 308.8 fs. The difference between the two models is 35.1 fs, with an error of 10.2%. We further examine the behavior of the models for Lorentzian pulses with FWHMs of 100 fs, 200 fs and 500 fs. The differences between the global and local models are 17.1 fs, 68.6 fs and 86.0 fs, respectively, with errors approximately around 17%. These comparative analyses clearly demonstrate the superior accuracy of the global model in intensity autocorrelation modeling.

Nonlinear Influence and Interaction Effect on the Imbalance of Metro-Oriented Dockless Bike-Sharing System

Dockless Bike-Sharing (DBS) is an eco-friendly, convenient, and popular form of ride-sharing. Metro-oriented DBS systems have the potential to promote sustainable transportation. However, the availability of DBS near metro stations often suffers from either scarcity or overabundance. To investigate the factors contributing to this imbalance, this paper examines the nonlinear influences and interactions that impact the DBS system near metro stations, with Shenzhen, China serving as a case study. An ensemble learning approach is employed to predict the imbalance state. Then, the machine learning interpretation method (i.e., SHapley Additive exPlanations) is used to quantify the contribution of effects, discover the strength of interactions between factors and uncover their underlying interactive connections. The results indicate the influence of external factors and the relations between pairwise variables (e.g., road density and the day of the week) for each imbalanced state. Provide two quantized sets of factors that can result in the supply-demand imbalance and support future transport planning decisions to enhance the accessibility and sustainability of Metro-oriented DBS systems.

A mechanical analysis model for tunnels under strike-slip faulting considering the fault zone width and nonlinear tunnel-stratum interaction

Tunnels crossing active fault zones are seriously damaged under the action of faulting. However, the influence of the fault zone width or nonlinear tunnel-stratum interaction is neglected in existing analytical models, resulting in incorrect estimation of the tunnel mechanical response. To aid in the seismic design of tunnels, a mechanical analysis model for tunnels under strike-slip faulting considering the effect of fault zone width and nonlinear tunnel-stratum interaction is first proposed in this work. The calculation results of the proposed model agree well with those obtained from the model test and numerical simulation, and the accuracy is obviously higher than that of the existing analytical methods. Compared with the FEM numerical model, the average errors of the peak bending moment, shear force and axial force calculated by the proposed model are 6.37 %, 11.00 % and 9.91 %, respectively. Neglecting the effect of fault zone width or nonlinear tunnel-stratum interaction, the tunnel response will be misestimated, e.g., when the fault displacement is 3 m and the crossing angle β is 90°, the overestimated value is approximately 40–110 %. Finally, the results of parameter analysis show that under the condition of 0° < β < 90°, the tunnel failure scope caused by the left-lateral strike-slip faulting is obviously larger than that caused by the right-lateral strike-slip faulting, while the conclusion is opposite under 90° < β < 180°; the maximum strain within the tunnel correlates directly with fault displacement and the strength of the fault zone, exhibiting an inverse correlation with the width of the fault zone; meanwhile, the scope for tunnel failure is directly influenced by fault displacement, fault zone width, and the crossing angle (where 90° <β < 180°), while inversely affected by the crossing angle (where 0° <β < 90°) and the strength of the fault zone.

Quantifying the heterogeneous impacts of the urban built environment on traffic carbon emissions: New insights from machine learning techniques

The configuration of the urban built environment is critical for promoting sustainability and achieving carbon neutrality. However, existing studies mostly use linear and spatial econometric models to investigate the relationship between urban built environments and traffic carbon dioxide (CO2) emissions, in-depth studies exploring the heterogeneous impacts of related features on traffic CO2 emission by interpretive machine learning models are scarce. Hence, we extract four dimensionless features to depict the size, compactness, irregularity, and isolation of built-up areas, and road network-related features (i.e., average cluster coefficient, road topological density, and road geometric density), respectively. Subsequently, we develop an interpretive machine learning framework based on the extracted features related to the urban built-up areas and road networks. The interpretive results of the proposed framework uncover that urban morphological features, especially population density (POP), GDP per capita (GDPpc), and urban physical compactness (UPC), have a heterogeneous impact on the per capita traffic emission (PCCE) across different cities. GDPpc is more like a linear relationship with PCCE, and UPC has a significant influence on PCCE when its value is between 62% and 78%. Our results also reveal the nonlinear relationships and interactive effects between these features, providing the implications of urban morphological planning and carbon emission reduction.

Role of “positive phase bunching” effect for long-term electron flux dynamics due to resonances with whistler-mode waves

Resonant interactions with electromagnetic whistler-mode waves are a primary driver of energetic electron dynamics in the Earth's radiation belts. The most intense waves can resonate with electrons nonlinearly, and effects of such nonlinear resonant interactions significantly differ from the classical quasi-linear diffusion. There have been continuous efforts on the theoretical investigation and implementation of these effects into radiation belt models, but not all nonlinear effects have been revealed yet. The two most investigated effects are phase trapping and phase bunching, which are responsible for electron acceleration and precipitation into the Earth's atmosphere, respectively, i.e., for the first cyclotron resonance with waves generated at the equator and propagating to higher latitudes, phase trapping increases electrons' energy, whereas phase bunching decreases the electron pitch-angle (and magnetic moment). However, recent studies reported a new effect called positive phase bunching, which may increase the electron pitch-angle and move them away from the loss-cone. This paper aims to characterize possible contributions of this effect to long-term electron dynamics, including multiple resonant interactions. Using an iterated mapping technique, we show that although the positive phase bunching effect can modify electron trajectories, it does not change the average rate of electron mixing in phase space. Thus, this effect may be safely neglected in long-term simulations of radiation belt dynamics. We also discuss possible verification of the positive phase bunching effect using short (single resonance), bursty electron precipitation events.

Unpacking the nonlinear relationships and interaction effects between urban environment factors and the urban nighttime heat index

In this study, we identified the urban environmental factors affecting the nighttime heat index (NHI), which has policy implications for improving the urban thermal environment using Smart Seoul Urban Data Sensor (S-DoT) data and an interpretable machine learning methodology. S-DoT sensors are ideal for deriving the heat index at a micro-scale in space and time, unlike ground-based observations and satellite-based imagery traditionally used to measure urban temperatures. Moreover, the interpretable machine learning methodology can overcome the nonlinearity argument of the influential factors identified in previous studies. The main results of this study are as follows. First, the Sky View Factor generally has a negative association with the NHI, which means that a higher SVF is associated with a lower NHI. Conversely, the surface roughness commonly has a positive association with the NHI, which signifies that a higher surface roughness results in a higher NHI. Second, the building view factor significantly increases the NHI, and the gross floor area of the building has a positive association with the NHI regardless of its use. Third, although the center of the city has a high temperature, if it has physical environment factors similar to the outskirts of the city, the NHI there may be relatively low compared to the nighttime air temperature. This study is meaningful because it empirically shows the nonlinear relationships and interaction effects between urban environment factors and the NHI and suggests policy implications to improve the urban nighttime thermal environment.

Understanding consumers' intentions to purchase smart clothing using PLS-SEM and fsQCA.

With the advancement of artificial intelligence (AI) and the Internet of Things (IoT), smart clothing, which has enormous growth potential, has developed to suit consumers' individualized demands in various areas. This paper aims to construct a model that integrates that technology acceptance model (TAM) and functionality-expressiveness-aesthetics (FEA) model to explore the key factors influencing consumers' smart clothing purchase intentions (PIs). Partial least squares structural equation modeling (PLS-SEM) was employed to analyze the data, complemented by fuzzy-set qualitative comparative analysis (fsQCA). The PLS-SEM results identified that the characteristics of functionality (FUN), expressiveness (EXP), and aesthetics (AES) positively and significantly affect perceived ease of use (PEOU), and only EXP affects perceived usefulness (PU). PU and PEOU positively impact consumers' attitudes (ATTs). Subsequently, PU and consumers' ATTs positively influence PIs. fsQCA revealed the nonlinear and complex interaction effects of the factors influencing consumers' smart clothing purchase behaviors and uncovered five necessary and six sufficient conditions for consumers' PIs. This paper furthers theoretical understanding by integrating the FEA model into the TAM. Additionally, on a practical level, it provides significant insights into consumers' intentions to purchase smart clothing. These findings serve as valuable tools for corporations and designers in strategizing the design and promotion of smart clothing. The results validate theoretical conceptions about smart clothing PIs and provide useful insights and marketing suggestions for smart clothing implementation and development. Moreover, this study is the first to explain smart clothing PIs using symmetric (PLS-SEM) and asymmetric (fsQCA) methods.

A quantitative exploration of the interactions and synergistic driving mechanisms between factors affecting regional air quality based on deep learning

Air pollution represents a significant environmental challenge on a global scale. The exploration of factors and mechanisms influencing air quality has garnered considerable attention and produced a substantial body of research. Nonetheless, the absence of effective research tools has resulted in a limited understanding of the nonlinear interactive effects of multiple factors on air quality, as well as their patterns and spatiotemporal variability characteristics. Furthermore, the efficacy of multifactor joint control strategies in practical air pollution management remains inadequate. A novel regional air environmental quality prediction model was developed utilizing a neural network with long short-term memory (LSTM) in deep learning based on an analysis of the spatiotemporal heterogeneity of regional air environmental quality in the Yangtze River Economic Belt (YEB). The model results were attributed and interpreted by integrating the SHapley Additive explanation (SHAP) method, focusing on the possible interactive effects and synergistic driving mechanisms of PM2.5 and O3 as the main pollutants and other factors on the air quality index (AQI) in a quantitative way, respectively. The SHAP interaction values of five factor pairs, namely PM2.5 and temperature, PM2.5 and precipitation, O3 and temperature, O3 and NO2, and O3 and PM2.5, are depicted in dependence scatter plots that exhibit three distinct trajectory shapes, namely linear, U-shaped, and irregular. The linear pattern of the dependence scatter plots for PM2.5 and precipitation in the YEB, midstream, and downstream regions, as well as for O3 and temperature in the upstream region, is evident. The irregular patterns of PM2.5 and precipitation, O3 and NO2, O3 and PM2.5 in the upstream, and PM2.5 and temperature in the downstream are observed to be correspondingly related. Additionally, a U-shaped pattern is exhibited by O3 and temperature in the YEB, midstream and downstream, PM2.5 and temperature in the upstream and midstream, O3 and NO2 in the YEB, midstream and downstream, and O3 and PM2.5 in the YEB. Of the three models, the U-shaped model's identification of inflection points and corresponding quantitative determination of factor thresholds hold greater practical implications for decision-making in air environment management. This pattern suggests that the synergistic effect of factor pairs initially decreases with changes in each factor but subsequently begins to increase after reaching inflection points. It is anticipated that this research will contribute to the advancement of theoretical inquiry into the nonlinear multifactor interaction effect and synergistic driving model of regional air quality. Additionally, it is expected to furnish a valuable foundation for decision-making in the development of joint air pollution prevention and control strategies aimed at addressing compound air pollution issues.

Machine learning and the prediction of changes in profitability

AbstractThis study uses machine‐learning methods to predict next‐period change in profitability based on a model proposed by Penman and Zhang (2004, Working paper, Columbia University and University of California, Berkeley; “PZ”). We find that new machine‐learning methods predict out of sample substantially better than traditional regression methods and provide richer interpretations about the role and impact of different predictor variables through their nonlinear relationships and interaction effects. For example, our results contrast with previous research by showing that both components of the DuPont decomposition (change in profit margin and change in asset turnover) are informative of next‐period changes in profitability. Our results are robust across different performance metrics, alternative machine‐learning models, and software. Furthermore, an unconstrained machine‐learning model using a larger feature space could not significantly improve the performance of the PZ model. PZ variables alone accounted for most of the explanatory power of the unconstrained model, suggesting the PZ model is both well specified (in terms of feature selection) and robust in higher dimensional settings. With respect to the economic significance of this information, we find mixed results. The market appears to adjust its expectations more in line with the machine‐learning predictions relative to the PZ model but the portfolio returns are not significantly different.

Sonic horizon formation for two-dimensional Bose–Einstein condensates with higher-order nonlinear interaction

Based on the Gross–Pitaevskii equation model that incorporates higher-order nonlinear interaction, we studied sonic black hole and sonic horizon formation involved in nonlinear dynamical evolution for Bose–Einstein condensates with higher-order nonlinear interaction. On the basis of the modified variational method and the scenario where the system starts dynamic evolution from ground state, we derived the typical system distribution width function, which is analytically formulated as periodic oscillation solution and monotonically damped variational oscillation solution under different parametric settings. We also calculated the criteria formula for sonic black hole horizon formation with regard to the two evolution modes: oscillation mode and monotonically decay mode, pictorially demonstrating the time interval of sonic horizon appearance. The theoretical results obtained here can be used to guide relevant experimental studies of sonic horizon and sonic black hole formation for Bose–Einstein condensates incorporating the higher-order nonlinear interaction effects.

Period-2 Thermoacoustics in a Swirl-Stabilised Partially Premixed Flame Computed Using Large Eddy Simulation

A partially premixed swirl-stabilised flame under thermoacoustically unstable conditions is studied using large eddy simulation with an unstrained flamelet model for the filtered reaction rate. The simulation results agree well with measured statistics of velocity, temperature and mixture fraction. Two thermoacoustic modes at approximately 300 and 590 Hz are excited for the case studied. The second mode pressure amplitude is comparable to that of the first mode. However, the second mode of heat release rate fluctuations is not as significant as for the pressure which results in a 2:1 frequency locking behaviour. The analysis offers insights into the physical mechanism involved in the excitation of the two modes and the 2:1 frequency locking behaviour. The index based on the Rayleigh Criterion in frequency domain is analysed to understand the coupling between the heat release rate and pressure fluctuations. It is observed that there is a nonlinear interaction between the two modes resulting in energy exchange across the two modes. The conventional Rayleigh Index has limitations in explaining the observed dynamics and therefore, a modified Rayleigh Index is defined to understand the effects of nonlinear mode interactions on thermoacoustic characteristics. A mode shape analysis using LES and acoustic-modelling reveals that the first mode may be a Helmholtz mode with internal damping that is excited by an acoustic source, and the second mode has the characteristic shape of a chamber mode.

Revealing Driving Factors of Urban O3 Based on Explainable Machine Learning

Driven by precursor emissions, meteorological conditions, and other factors, atmospheric ozone (O3) has become the main pollutant affecting urban air quality in summer. The current deductive models driven by physical and chemical mechanisms require a large number of parameters for the analysis of O3 pollution, and the calculation timeliness is poor. The data-driven inductive models are efficient but have problems such as poor explanation. In this study, an explainable model of data-driven Correlation-ML-SHAP was established to reveal the strongly correlated influencing factors of O3 concentration. Additionally, the machine learning ML module coupled with the explainable SHAP module was used to calculate the contributions of driving factors to O3 concentration, so as to realize the quantitative analysis of driving factors. The O3 pollution process in the summer of 2021 in Jincheng City was used as an example to carry out the application research. The results showed that the Correlation-ML-SHAP model could reveal and use strong driving factors to simulate O3 concentration and quantify influence contribution, and the ML module used the XGBoost model to achieve the best simulation accuracy. Air temperature, solar radiation, relative humidity, and precursor emission level were the strong driving factors of O3 pollution in Jincheng City in summer 2021, and the contribution weights were 32.1%, 21.3%, 16.5%, and 15.6%. The contribution weights of air temperature, solar radiation, and precursor emission level increased by 3.4%, 1.2%, and 1.2% on polluted days, respectively, and the contribution weights of precursor emission level rose to third place on polluted days. Each driving factor had a nonlinear interaction effect on O3 concentration. When the air temperature exceeded 24℃, or the relative humidity was lower than 70%, there was a 94.9% and 94.1% probability of positive contribution to O3 pollution, respectively. Under such meteorological conditions, ρ(NO2) exceeded 9 μg·m-3, or ρ(CO) exceeded 0.7 mg·m-3, and there was a 94.9% and 99.3% probability of positive contribution to O3 pollution, respectively. The southeast wind speed was lower than 5.8 m·s-1, or the south wind speed was lower than 5.3 m·s-1, both of which contributed positively to O3 pollution. The model quantitatively analyzed the influence contribution of various driving factors on urban O3 concentration, which could provide a basis for the prevention and control of urban atmospheric O3 pollution in summer.

Forecasting nonlinear dependency between cryptocurrencies and foreign exchange markets using dynamic copula: evidence from GAS models

PurposeThis paper examines and forecasts correlations between cryptocurrencies and major fiat currencies using Generalized Autoregressive Score (GAS) time-varying copulas. The authors examine to which extent the multivariate GAS method captures the volatility persistence and the nonlinear interaction effects between cryptocurrencies and major fiat currencies.Design/methodology/approachThe authors model tail dependence between conventional currencies and Bitcoin utilizing a Glosten-Jagannathan-Runkle Generalized Autoregressive Conditional Heteroscedastic model (GJR-GARCH)-GAS copula specification, which allows detecting the leptokurtic feature and clustering effects of currency returns distribution.FindingsThe authors' results show evidence of multiple tail dependence regimes, implying the unsuitability of applying static models to entirely describe the extreme dependence between Bitcoin and fiat currencies. Compared to the most common constant copulas, the authors find that the multivariate GAS copulas better forecast the volatility and dependency between cryptocurrencies and foreign exchange markets. Furthermore, based on the value-at-risk (VaR) and expected shortfall (ES) analyses, the authors show that the multivariate GAS models produce accurate risk measures by adding cryptocurrencies to a portfolio of fiat currencies.Originality/valueThis paper has two main contributions to the existing literature on cryptocurrencies. First, the authors empirically examine the tail dependence structure between common conventional currencies and bitcoin using GJR-GARCH GAS copulas which consider the leptokurtic feature and clustering effects of currency returns distribution. Second, by modeling VaR and ES, the authors test the implication of using time-varying models on the performance of currency portfolios, including cryptocurrencies.

Non-linear soil-structure interaction effect on the seismic response of a building

Non-linear soil-structure interaction effect on the seismic response of a building

The effect of non-linear competitive interactions on quantifying niche and fitness differences

The niche and fitness differences of modern coexistence theory separate mechanisms into stabilizing and equalizing components. Although this decomposition can help us predict and understand species coexistence, the extent to which mechanistic inference is sensitive to the method used to partition niche and fitness differences remains unclear. We apply two alternative methods to assess niche and fitness differences to four well-known community models. We show that because standard methods based on linear approximations do not capture the full community dynamics, they can sometimes lead to incorrect predictions of coexistence and misleading interpretations of stabilizing and equalizing mechanisms. Specifically, they fail when both species occupy the same niche or in the presence of positive frequency dependence. Conversely, a more recently developed method to decompose niche and fitness differences, which accounts for the full non-linear dynamics of competition, consistently identifies the correct contribution of stabilizing and equalizing components. This approach further reveals that when the true complexity of the system is taken into account, essentially all mechanisms comprise both stabilizing and equalizing components and that local maxima and minima of stabilizing and equalizing mechanisms exist. Amidst growing interest in the role of non-additive and higher order interactions in regulating species coexistence, we propose that the effective decomposition of niche and fitness differences will become increasingly reliant on methods that account for the inherent non-linearity of community dynamics.