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Question Number 207139 by Wuji last updated on 07/May/24

Two proteins (x&y) control each other through mutual repression. the dynamic model for the system consists of the following system of ODEs. calculate the steady state values of these two peoteins. comment of the stabilityof the steady state and the type of phase of portrait expected foe this system. consider x,y≥0 (dx/dt)=(y/(1+y))−2x (dy/dt)=(x/(1+x))−y

$$ \\ $$$$\mathrm{Two}\:\mathrm{proteins}\:\left(\mathrm{x\&y}\right)\:\mathrm{control}\:\mathrm{each} \\ $$$$\mathrm{other}\:\mathrm{through}\:\mathrm{mutual}\:\mathrm{repression}.\:\mathrm{the} \\ $$$$\mathrm{dynamic}\:\mathrm{model}\:\mathrm{for}\:\mathrm{the}\:\mathrm{system}\:\mathrm{consists}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{system}\:\mathrm{of}\:\mathrm{ODEs}. \\ $$$$\mathrm{calculate}\:\mathrm{the}\:\mathrm{steady}\:\mathrm{state}\:\mathrm{values}\:\mathrm{of}\:\mathrm{these}\:\mathrm{two}\:\mathrm{peoteins}.\: \\ $$$$\mathrm{comment}\:\mathrm{of}\:\mathrm{the}\:\mathrm{stabilityof}\:\mathrm{the}\:\mathrm{steady}\:\mathrm{state} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{type}\:\mathrm{of}\:\mathrm{phase}\:\mathrm{of}\:\mathrm{portrait}\:\mathrm{expected}\:\mathrm{foe}\:\mathrm{this} \\ $$$$\mathrm{system}.\:\mathrm{consider}\:\mathrm{x},\mathrm{y}\geqslant\mathrm{0} \\ $$$$\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{\mathrm{y}}{\mathrm{1}+\mathrm{y}}−\mathrm{2x}\:\:\:\frac{\mathrm{dy}}{\mathrm{dt}}=\frac{\mathrm{x}}{\mathrm{1}+\mathrm{x}}−\mathrm{y} \\ $$

Answered by Berbere last updated on 07/May/24

too complecated to read Your poste police Too big

$${too}\:{complecated}\:\:{to}\:{read}\:{Your}\:{poste} \\ $$$${police}\:{Too}\:{big} \\ $$

Commented by Wuji last updated on 07/May/24

you can click on fit width to read clear, sir

$$\mathrm{you}\:\mathrm{can}\:\mathrm{click}\:\mathrm{on}\:\mathrm{fit}\:\mathrm{width}\:\mathrm{to}\:\mathrm{read}\:\mathrm{clear},\:\mathrm{sir} \\ $$

Commented by mr W last updated on 07/May/24

Commented by mr W last updated on 07/May/24

“fit width” doesn′t work when commenting or answering a post. please use default font size 20. please use line breaks.

$$``{fit}\:{width}''\:{doesn}'{t}\:{work}\:{when} \\ $$$${commenting}\:{or}\:{answering}\:{a}\:{post}. \\ $$$$ \\ $$$${please}\:{use}\:{default}\:{font}\:{size}\:\mathrm{20}. \\ $$$${please}\:{use}\:{line}\:{breaks}. \\ $$

Commented by Wuji last updated on 07/May/24

please, sir. how can i make it looks nlrmal. i have put the font size to 20

$$\mathrm{please},\:\mathrm{sir}.\:\mathrm{how}\:\mathrm{can}\:\mathrm{i}\:\mathrm{make}\:\mathrm{it}\:\mathrm{looks}\: \\ $$$$\mathrm{nlrmal}.\:\mathrm{i}\:\mathrm{have}\:\mathrm{put}\:\mathrm{the}\:\mathrm{font}\:\mathrm{size}\:\mathrm{to}\:\mathrm{20} \\ $$

Commented by mr W last updated on 07/May/24

this looks normal now. thanks!

$${this}\:{looks}\:{normal}\:{now}.\:{thanks}! \\ $$

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