To further investigate the behaviour of the stability of the system while multiple parameters were varied, we constructed the characteristic polynomial of the Jacobian evaluated at each steady state (J ) and determined the stability of each steady state using the Routh-Hurwitz criterion, a preferred method for nonlinear ODE systems, which uses the coefficients of J and hence bypasses solving the roots of each polynomial [45,46].
Sample text:```We consider as unknown true system the half-load model of the flexible transmission system used as a benchmark in a special issue of the European Journal of Control (Landau et al., 1995b).```
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Sample text:```Finding optimal paths in dynamic environments has attracted significant attention in the robotics community (See Latombe (1990); LaValle (1999); Lu et al (2015); Jur (2007) and the references therein).```
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Sample text:```We consider as unknown true system the half-load model of the flexible transmission system used as a benchmark in a special issue of the European Journal of Control (Landau et al., 1995b).```
Sample intent: background



Sample text:```In-between methods can be subdivided into linear approximations [12,24] and quadratic interpolation methods [22,23,25–27] based on the degree of the polynomial approximation employed.```
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Sample text:```This seems to be the main drawback of the current implementation in comparison to the method of Black Jepson (“refined” in Table 1).```
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Sample text:```However, it was found that the behaviors on the insulator surface showed nonlinear properties during the flashover process [20].```
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Sample text:```This seems to be the main drawback of the current implementation in comparison to the method of Black Jepson (“refined” in Table 1).```
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Sample text:```Discrepancies analogous to those between our results and those of simulations have, indeed, recently been observed in the case of the binary perceptron [18], the pspin interaction spin glass [19], and in the case of fluctuating manifolds in random media [20], where dynamically frozen phases were observed in regions of parameter space in which static approaches yielded ergodic phases.```
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Sample text:```This section contains a generalisation of the basic results on multifractal products of stochastic processes developed in Kahane (1985), Kahane (1987) and Mannersalo et al (2002).```
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Sample text:```The existence of time delay may lead to some more complicated dynamic behaviors such as oscillation, divergence, chaos, instability or other poor performance of the neural networks [6].```
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Sample text:```Finding optimal paths in dynamic environments has attracted significant attention in the robotics community (See Latombe (1990); LaValle (1999); Lu et al (2015); Jur (2007) and the references therein).```
Sample intent: method



Sample text:```For seeking the optimal value of Wh of the sub-problems which corresponds to the h-th level, we can solve the problem by the smoothing proximal gradient (SPG) method [6] fortunately.```
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Sample text:```A rook pivoting scheme as in [3] and [11] can be implemented for tridiagonal matrices, but a full rook scheme for general banded matrices would probably lead to a ”chasing” scheme as in [5] or [15] .```
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Sample text:```The present observations support and extend earlier contentions that Parkinson patients prefer to adopt a closedloop control mode, adjusting their movements continuously on the basis of available visual information (Flowers 1976).```
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Sample text:```In this study, we generalized previous results regarding the quasi-Gaussian shape and the scalar property using the SBF model [13,21,52].```
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Sample text:```We consider as unknown true system the half-load model of the flexible transmission system used as a benchmark in a special issue of the European Journal of Control (Landau et al., 1995b).```
Sample intent: background