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So, for small values of the BK conductance, the dynamical source of instability in the model is rooted in homoclinic bifurcations of a saddle equilibrium state, which suggests explicitly that the given model falls into a category of the so-called square-wave bursters introduced for 3D neuronal models [37, 38]. Figure 4 Bifurcations of oscillatory dynamics in the deterministic model.
For β diversity, there is a substantial positive effect of linguistic diversity on instability in the model.
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There was no instability in the models that would indicate collinearity.
For example, the appearance of a Benjamin-Feir instability in the Sel'kov model indicates the occurrence of spatio-temporal chaos which is mostly absent in the MWC model.
The instability inherent in the model is therefore actively utilised to provide energy-efficient transitions between configurations of the mechanism.
Our main result (see Theorem 5.1) indicates that chemotaxis-driven nonlinear instability occurs in the model (1.2), that is, nonlinear patterns are created by chemotaxis for the model (1.2) with nonlinear diffusion.
It provides insight into the properties of the instability in the numerical model and clarifies the parameters that influence its presence.
Recently, Fu et al. in [16] and [17] studied nonlinear instability in the Keller Segel model with a logistic source and cubic source term, respectively.
Also, adjusting only porosity avoids difficulty with numerical instability in the flow model caused by the addition of correlated parameters (porosity and hydraulic conductivity).
The existence of structures referred to as critical fragments in the bipartite digraph of a biochemical mechanism is necessary for the existence of multistability or Turing instability in the DE model [ 2- 4].
To ensure that the precision of the estimates was not affected by including the covariates listed above, we made sure that there were no signs of instability in the fitted model, such as unusually large estimates or standard errors.
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