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numerical ode analysis program pplane8  (MathWorks Inc)


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    MathWorks Inc numerical ode analysis program pplane8
    The separatrix and its approximations for system (9). a, <t>b</t> <t>pplane8</t> plots of (9) with parameters a Pr1 and b Pr2. The descending green curve in each graph is the pplane approximation of the stable manifold (separatrix M), and the ascending orange curve is the pplane approximation of the unstable manifold, U. The blue curves represent forward solutions of the system. The red curves represent the contours at which the self-renewal probability p = 0.5. Note that solutions to the right of the separatrix tend to nonzero (S, a), whereas solutions to the left tend to P1(0, 0). In each region, however, if the current values (S, a) are above the p = 0.5 contour, then S increases in time. Analogously, if (S, a) lies below the p = 0.5 contour, then S decreases. c, d The separatrices predicted by pplane8 (large dash, green) of c Pr1 and d Pr2 are plotted along with the SMT approximation of the separatrix, M* (solid black), the quadratic approximation, Mq∗ (small dash, blue), and the linear approximation, Ml∗ (cross, red) (Color figure online)
    Numerical Ode Analysis Program Pplane8, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/result/numerical ode analysis program pplane8/product/MathWorks Inc
    Average 90 stars, based on 1 article reviews
    numerical ode analysis program pplane8 - by Bioz Stars, 2026-04
    90/100 stars

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    1) Product Images from "Feedback Regulation in a Cancer Stem Cell Model can Cause an Allee Effect"

    Article Title: Feedback Regulation in a Cancer Stem Cell Model can Cause an Allee Effect

    Journal: Bulletin of mathematical biology

    doi: 10.1007/s11538-016-0161-5

    The separatrix and its approximations for system (9). a, b pplane8 plots of (9) with parameters a Pr1 and b Pr2. The descending green curve in each graph is the pplane approximation of the stable manifold (separatrix M), and the ascending orange curve is the pplane approximation of the unstable manifold, U. The blue curves represent forward solutions of the system. The red curves represent the contours at which the self-renewal probability p = 0.5. Note that solutions to the right of the separatrix tend to nonzero (S, a), whereas solutions to the left tend to P1(0, 0). In each region, however, if the current values (S, a) are above the p = 0.5 contour, then S increases in time. Analogously, if (S, a) lies below the p = 0.5 contour, then S decreases. c, d The separatrices predicted by pplane8 (large dash, green) of c Pr1 and d Pr2 are plotted along with the SMT approximation of the separatrix, M* (solid black), the quadratic approximation, Mq∗ (small dash, blue), and the linear approximation, Ml∗ (cross, red) (Color figure online)
    Figure Legend Snippet: The separatrix and its approximations for system (9). a, b pplane8 plots of (9) with parameters a Pr1 and b Pr2. The descending green curve in each graph is the pplane approximation of the stable manifold (separatrix M), and the ascending orange curve is the pplane approximation of the unstable manifold, U. The blue curves represent forward solutions of the system. The red curves represent the contours at which the self-renewal probability p = 0.5. Note that solutions to the right of the separatrix tend to nonzero (S, a), whereas solutions to the left tend to P1(0, 0). In each region, however, if the current values (S, a) are above the p = 0.5 contour, then S increases in time. Analogously, if (S, a) lies below the p = 0.5 contour, then S decreases. c, d The separatrices predicted by pplane8 (large dash, green) of c Pr1 and d Pr2 are plotted along with the SMT approximation of the separatrix, M* (solid black), the quadratic approximation, Mq∗ (small dash, blue), and the linear approximation, Ml∗ (cross, red) (Color figure online)

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    numerical ode analysis program pplane8  (MathWorks Inc)
    90
    MathWorks Inc numerical ode analysis program pplane8
    The separatrix and its approximations for system (9). a, <t>b</t> <t>pplane8</t> plots of (9) with parameters a Pr1 and b Pr2. The descending green curve in each graph is the pplane approximation of the stable manifold (separatrix M), and the ascending orange curve is the pplane approximation of the unstable manifold, U. The blue curves represent forward solutions of the system. The red curves represent the contours at which the self-renewal probability p = 0.5. Note that solutions to the right of the separatrix tend to nonzero (S, a), whereas solutions to the left tend to P1(0, 0). In each region, however, if the current values (S, a) are above the p = 0.5 contour, then S increases in time. Analogously, if (S, a) lies below the p = 0.5 contour, then S decreases. c, d The separatrices predicted by pplane8 (large dash, green) of c Pr1 and d Pr2 are plotted along with the SMT approximation of the separatrix, M* (solid black), the quadratic approximation, Mq∗ (small dash, blue), and the linear approximation, Ml∗ (cross, red) (Color figure online)
    Numerical Ode Analysis Program Pplane8, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/result/numerical ode analysis program pplane8/product/MathWorks Inc
    Average 90 stars, based on 1 article reviews
    numerical ode analysis program pplane8 - by Bioz Stars, 2026-04
    90/100 stars
    		  Buy from Supplier

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    The separatrix and its approximations for system (9). a, b pplane8 plots of (9) with parameters a Pr1 and b Pr2. The descending green curve in each graph is the pplane approximation of the stable manifold (separatrix M), and the ascending orange curve is the pplane approximation of the unstable manifold, U. The blue curves represent forward solutions of the system. The red curves represent the contours at which the self-renewal probability p = 0.5. Note that solutions to the right of the separatrix tend to nonzero (S, a), whereas solutions to the left tend to P1(0, 0). In each region, however, if the current values (S, a) are above the p = 0.5 contour, then S increases in time. Analogously, if (S, a) lies below the p = 0.5 contour, then S decreases. c, d The separatrices predicted by pplane8 (large dash, green) of c Pr1 and d Pr2 are plotted along with the SMT approximation of the separatrix, M* (solid black), the quadratic approximation, Mq∗ (small dash, blue), and the linear approximation, Ml∗ (cross, red) (Color figure online)

    Journal: Bulletin of mathematical biology

    Article Title: Feedback Regulation in a Cancer Stem Cell Model can Cause an Allee Effect

    doi: 10.1007/s11538-016-0161-5

    Figure Lengend Snippet: The separatrix and its approximations for system (9). a, b pplane8 plots of (9) with parameters a Pr1 and b Pr2. The descending green curve in each graph is the pplane approximation of the stable manifold (separatrix M), and the ascending orange curve is the pplane approximation of the unstable manifold, U. The blue curves represent forward solutions of the system. The red curves represent the contours at which the self-renewal probability p = 0.5. Note that solutions to the right of the separatrix tend to nonzero (S, a), whereas solutions to the left tend to P1(0, 0). In each region, however, if the current values (S, a) are above the p = 0.5 contour, then S increases in time. Analogously, if (S, a) lies below the p = 0.5 contour, then S decreases. c, d The separatrices predicted by pplane8 (large dash, green) of c Pr1 and d Pr2 are plotted along with the SMT approximation of the separatrix, M* (solid black), the quadratic approximation, Mq∗ (small dash, blue), and the linear approximation, Ml∗ (cross, red) (Color figure online)

    Article Snippet: Since it is cumbersome to further improve the approximation iteratively by the SMT, we check whether M * is a good approximation of M by comparing M * with the separatrix predicted for a given set of parameters by a numerical ODE analysis program (here we have used pplane8 in MATLAB; Arnold and Polking 1999 ).

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