Interpretation of a difference equation

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I'm using Sparse identification of nonlinear dynamics (SINDy) to identify the dynamics of some time series data. Please consider the following examples:



Example 1: ts1



Example 2: ts2



Example 3: ts3



Despite of the curve dissimilarities, the dynamics of these time series are very alike. The difference equations identified with SINDy for the above three cases are the following:



$x_k = 1.986 x_k-1 - 0.996 x_k-2$



$x_k = 1.986 x_k-1 - 0.995 x_k-2$



$x_k = 1.983 x_k-1 - 0.991 x_k-2$



If I'm correct, this roughly translates to the following differential equation:



$displaystylefracdxdt - fracd^2xdt^2 = 0$



How should I interpret this?



Are there physical phenomena which are described by this equation?




differential-equations recurrence-relations time-series




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  • Why the downvote?
    – xufoy
    Jul 18 at 17:31














up vote
-1
down vote

favorite












I'm using Sparse identification of nonlinear dynamics (SINDy) to identify the dynamics of some time series data. Please consider the following examples:



Example 1: ts1



Example 2: ts2



Example 3: ts3



Despite of the curve dissimilarities, the dynamics of these time series are very alike. The difference equations identified with SINDy for the above three cases are the following:



$x_k = 1.986 x_k-1 - 0.996 x_k-2$



$x_k = 1.986 x_k-1 - 0.995 x_k-2$



$x_k = 1.983 x_k-1 - 0.991 x_k-2$



If I'm correct, this roughly translates to the following differential equation:



$displaystylefracdxdt - fracd^2xdt^2 = 0$



How should I interpret this?



Are there physical phenomena which are described by this equation?




differential-equations recurrence-relations time-series




share|cite|improve this question



















  • Why the downvote?
    – xufoy
    Jul 18 at 17:31












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











I'm using Sparse identification of nonlinear dynamics (SINDy) to identify the dynamics of some time series data. Please consider the following examples:



Example 1: ts1



Example 2: ts2



Example 3: ts3



Despite of the curve dissimilarities, the dynamics of these time series are very alike. The difference equations identified with SINDy for the above three cases are the following:



$x_k = 1.986 x_k-1 - 0.996 x_k-2$



$x_k = 1.986 x_k-1 - 0.995 x_k-2$



$x_k = 1.983 x_k-1 - 0.991 x_k-2$



If I'm correct, this roughly translates to the following differential equation:



$displaystylefracdxdt - fracd^2xdt^2 = 0$



How should I interpret this?



Are there physical phenomena which are described by this equation?




differential-equations recurrence-relations time-series




share|cite|improve this question











I'm using Sparse identification of nonlinear dynamics (SINDy) to identify the dynamics of some time series data. Please consider the following examples:



Example 1: ts1



Example 2: ts2



Example 3: ts3



Despite of the curve dissimilarities, the dynamics of these time series are very alike. The difference equations identified with SINDy for the above three cases are the following:



$x_k = 1.986 x_k-1 - 0.996 x_k-2$



$x_k = 1.986 x_k-1 - 0.995 x_k-2$



$x_k = 1.983 x_k-1 - 0.991 x_k-2$



If I'm correct, this roughly translates to the following differential equation:



$displaystylefracdxdt - fracd^2xdt^2 = 0$



How should I interpret this?



Are there physical phenomena which are described by this equation?





differential-equations recurrence-relations time-series





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 18 at 16:44









xufoy

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  • Why the downvote?
    – xufoy
    Jul 18 at 17:31
















  • Why the downvote?
    – xufoy
    Jul 18 at 17:31















Why the downvote?
– xufoy
Jul 18 at 17:31




Why the downvote?
– xufoy
Jul 18 at 17:31















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