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>Model

ID:(2134, 0)

Description

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When social and political conflicts intensify, governments typically increase spending and borrowing to try to maintain order, and wealth gaps tend to widen. Debt rises when trust in institutions declines (as governments borrow more to preserve stability) and also when wealth inequality increases (due to pressures for redistribution and populist demands).

For these reasons, we assume that debt dynamics can be modeled as the variation of the debt Index ($I_d$) with respect to the time ($t$) as a function of the trust Index ($I_t$) and the wealth Gap Index ($I_w$):

where the constants the increase debt with confidence ($c_{dt}$) and the increase in debt depends on the wealth gap ($c_{dw}$) apply.

ID:(16147, 0)

Description

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As a countrys debt rises and the value of its currency declines, it typically loses its reserve currency status. Higher debt increases the risk of currency devaluation (through money printing and loss of credibility), while the loss of reserve currency status accelerates devaluation (due to reduced foreign demand for the currency).

For these reasons, we assume that devaluation dynamics can be modeled as the variation of the devaluation index ($I_c$) with respect to the time ($t$) as a function of the debt Index ($I_d$) and the reserve Currency Index ($I_r$):

where the constants the increased devaluation due to debt ($c_{cd}$) and the reduction of devaluation by reverse currency role ($c_{cr}$) apply.

ID:(16148, 0)

Description

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The strengths of empires derive from their education, innovation, economic output, and military might, while their weaknesses stem from high debt levels, internal conflicts, and loss of competitiveness. Economic power grows through innovation and military protection and declines with excessive debt and internal unrest.

For these reasons, we assume that economic power dynamics can be modeled as the variation of the economic Power Index ($I_p$) with respect to the time ($t$) as a function of the index of Innovation ($I_i$), the index of Military Strength ($I_m$), the debt Index ($I_d$), and the index of Unrest ($I_u$):

where the constants the increased economic power through innovation ($c_{pi}$), the increased economic power through military strength ($c_{pm}$), the reduction of economic power due to devaluation ($c_{pc}$), and the reduction of economic power due to debt ($c_{pd}$) apply.

ID:(16149, 0)

Description

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The early stages of a rising empire are characterized by strong education systems. As wealth gaps widen over time, education often becomes less effective for the majority. Investment in education is stronger when debt levels are low (allowing more resources for development), while a growing wealth gap often leads to the deterioration of public education.

For these reasons, we assume that education dynamics can be modeled as the variation of the education Index ($I_e$) with respect to the time ($t$) as a function of the debt Index ($I_d$) and the wealth Gap Index ($I_w$):

where the constants the increase in education due to economic power ($c_{ep}$) and the reduction in education due to the wealth gap ($c_{ew}$) apply.

ID:(16150, 0)

Description

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Strong education systems and a commitment to innovation are the foundations of economic competitiveness. Devaluation discourages investment in research and development. Innovation stems from education and declines when currency devaluation destabilizes investments and institutions.

For these reasons, we assume that innovation dynamics can be modeled as the variation of the index of Innovation ($I_i$) with respect to the time ($t$) as a function of the education Index ($I_e$) and the devaluation index ($I_c$):

where the constants the increasing innovation through existing education ($c_{ie}$) and the increased innovation due to economic power ($c_{ip}$) apply.

ID:(16151, 0)

Description

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Military strength depends on the economic base. As empires decline economically, their military strength often weakens. Military power relies on economic strength (to afford modern forces), while devaluation undermines military funding and capabilities.

For these reasons, we assume that military strength dynamics can be modeled as the variation of the index of Military Strength ($I_m$) with respect to the time ($t$) as a function of the economic Power Index ($I_p$) and the devaluation index ($I_c$):

where the constants the increased military development due to economic power ($c_{mp}$) and the reduction of military development due to devaluation ($c_{mc}$) apply.

ID:(16152, 0)

Description

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The value of a reserve currency is driven by the relative strength of the empires economy, its military, and the trustworthiness of its system. Maintaining economic power, military dominance, and institutional trust supports a strong reserve currency, while devaluation undermines it.

For these reasons, we assume that reserve currency dynamics can be modeled as the variation of the reserve Currency Index ($I_r$) with respect to the time ($t$) as a function of the economic Power Index ($I_p$), the index of Military Strength ($I_m$), the trust Index ($I_t$), and the devaluation index ($I_c$):

where the constants the increase in being the Reserve Currency for being an Economic Power ($c_{rp}$), the increase in Reserve Currency due to Military Strength ($c_{rm}$), the reduction of reserve currency due to debt ($c_{rd}$), and the reduction of being the Reserve Currency due to Devaluation ($c_{rc}$) apply.

ID:(16153, 0)

Description

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When internal conflict increases, trust in leadership declines, and wealth gaps widen, the social cohesion necessary to maintain order weakens. Trust strengthens when unrest is low and deteriorates as wealth gaps and debt burdens rise.

For these reasons, we assume that trust dynamics can be modeled as the variation of the trust Index ($I_t$) with respect to the time ($t$) as a function of the index of Unrest ($I_u$), the wealth Gap Index ($I_w$), and the debt Index ($I_d$):

where the constants the coefficient of confidence for discomfort reduction ($c_{tu}$), the reduction of trust due to oppression ($c_{to}$), and the reduction of confidence with the level of indebtedness ($c_{td}$) apply.

ID:(16154, 0)

Description

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As wealth gaps widen and trust in institutions erodes, unrest typically increases. Governments often respond by tightening control, which can suppress but not fully eliminate underlying tensions. Unrest grows with increasing wealth inequality and loss of trust, and it is temporarily suppressed through state oppression.

For these reasons, we assume that unrest dynamics can be modeled as the variation of the index of Unrest ($I_u$) with respect to the time ($t$) as a function of the wealth Gap Index ($I_w$), the trust Index ($I_t$), and the oppression index ($I_o$):

where the constants the wealth gap riots on the rise ($c_{uw}$), the reducing unrest through trust ($c_{ut}$), and the reduction of oppression riots ($c_{uo}$) apply.

ID:(16155, 0)

Description

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As unrest grows, leaders tend to restrict freedoms in an effort to maintain order, often fueling a downward spiral. Government oppression rises directly in response to increasing unrest.

For these reasons, we assume that oppression dynamics can be modeled as the variation of the oppression index ($I_o$) with respect to the time ($t$) as a function of the index of Unrest ($I_u$):

where the constant the increased oppression due to riots ($c_{ou}$) applies.

ID:(16156, 0)

Description

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Declines in education quality and economic devaluations tend to widen wealth gaps, deepening divisions within society. Inequality grows when education fails (reducing social mobility), and devaluation (through inflation and asset protection for the wealthy) exacerbates the wealth gap.

For these reasons, we assume that wealth gap dynamics can be modeled as the variation of the wealth Gap Index ($I_w$) with respect to the time ($t$) as a function of the education Index ($I_e$) and the devaluation index ($I_c$):

where the constants the widening wealth gap with economic power ($c_{wp}$) and the reducing the wealth gap through devaluation ($c_{wc}$) apply.

ID:(16157, 0)

Equation

>Top, >Model

The debt Index ($I_d$) varies with the time ($t$) as a function of the devaluation index ($I_c$), the economic Power Index ($I_p$), the reserve Currency Index ($I_r$), the index of Innovation ($I_i$), and the trust Index ($I_t$):

$\displaystyle\frac{ dI_d }{ dt } = c_{dc} (1- I_c ) + c_{dp} I_p + c_{dr} I_r + c_{di} I_i + c_{dt} I_t $

Conditions

Variables

Relation

Typical values for the debt reduction with devaluation ($c_{dc}$), the increase debt with economic power ($c_{dp}$), the increase debt with reserve currency ($c_{dr}$), the increase debt with innovation ($c_{di}$), and the increase debt with confidence ($c_{dt}$) are approximately 0.015, 0.015, 0.010, 0.008, and 0.013 per year, respectively.

ID:(16136, 0)

Equation

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The devaluation index ($I_c$) varies with the time ($t$) as a function of the debt Index ($I_d$) and the reserve Currency Index ($I_r$):

$\displaystyle\frac{ dI_c }{ dt } = c_{cd} I_d + c_{cr} (1- I_r )$

Conditions

Variables

Relation

Typical values of the increased devaluation due to debt ($c_{cd}$) and the reduction of devaluation by reverse currency role ($c_{cr}$) are on the order of 0.05 and 0.04 per year, respectively.

ID:(16137, 0)

Equation

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The economic Power Index ($I_p$) varies in the time ($t$) as a function of the index of Innovation ($I_i$), the index of Military Strength ($I_m$), the debt Index ($I_d$), and the index of Unrest ($I_u$):

$\displaystyle\frac{ dI_p }{ dt } = c_{pi} I_i + c_{pm} I_m - c_{pd} I_d - c_{pu} I_u $

Conditions

Variables

Relation

Typical values of the increased economic power through innovation ($c_{pi}$), the increased economic power through military strength ($c_{pm}$), the reduction of economic power due to devaluation ($c_{pc}$), and the reduction of economic power due to debt ($c_{pd}$) are on the order of 0.08, 0.05, 0.03, and 0.04 per year, respectively.

ID:(16141, 0)

Equation

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The education Index ($I_e$) varies with the time ($t$) as a function of the debt Index ($I_d$) and the wealth Gap Index ($I_w$):

$\displaystyle\frac{ dI_e }{ dt } = c_{ed} (1- I_d ) - c_{ew} I_w $

Conditions

Variables

Relation

Typical values of the increase in education due to economic power ($c_{ep}$) and the reduction in education due to the wealth gap ($c_{ew}$) are on the order of 0.05 and 0.02 per year, respectively.

ID:(16138, 0)

Equation

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The index of Innovation ($I_i$) varies with the time ($t$) as a function of the education Index ($I_e$) and the devaluation index ($I_c$):

$\displaystyle\frac{ dI_i }{ dt } = c_{ie} I_e - c_{ic} I_c $

Conditions

Variables

Relation

Typical values of the increasing innovation through existing education ($c_{ie}$) and the increased innovation due to economic power ($c_{ip}$) are on the order of 0.10 and 0.05 per year, respectively.

ID:(16139, 0)

Equation

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The index of Military Strength ($I_m$) varies with the time ($t$) as a function of the economic Power Index ($I_p$) and the devaluation index ($I_c$):

$\displaystyle\frac{ dI_m }{ dt } = c_{mp} I_p - c_{mc} I_c $

Conditions

Variables

Relation

Typical values of the increased military development due to economic power ($c_{mp}$) and the reduction of military development due to devaluation ($c_{mc}$) are on the order of 0.07 and 0.04 per year, respectively.

ID:(16140, 0)

Equation

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The reserve Currency Index ($I_r$) varies with the time ($t$) as a function of the economic Power Index ($I_p$), the index of Military Strength ($I_m$), the trust Index ($I_t$), and the devaluation index ($I_c$):

$\displaystyle\frac{ dI_r }{ dt } = c_{rp} I_p + c_{rm} I_m + c_{rt} I_t - c_{rc} I_c $

Conditions

Variables

Relation

Typical values of the increase in being the Reserve Currency for being an Economic Power ($c_{rp}$), the increase in Reserve Currency due to Military Strength ($c_{rm}$), the reduction of reserve currency due to debt ($c_{rd}$), and the reduction of being the Reserve Currency due to Devaluation ($c_{rc}$) are on the order of 0.06, 0.06, 0.06, and 0.07 per year, respectively.

ID:(16142, 0)

Equation

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The trust Index ($I_t$) varies in the time ($t$) as a function of the index of Unrest ($I_u$), the wealth Gap Index ($I_w$), and the debt Index ($I_d$):

$\displaystyle\frac{ dI_t }{ dt } = c_{tu} (1- I_u ) - c_{tw} I_w - c_{td} I_d $

Conditions

Variables

Relation

Typical values of the coefficient of confidence for discomfort reduction ($c_{tu}$), the reduction of trust due to oppression ($c_{to}$), and the reduction of confidence with the level of indebtedness ($c_{td}$) are on the order of 0.08, 0.05, and 0.04 per year, respectively.

ID:(16143, 0)

Equation

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The index of Unrest ($I_u$) varies with the time ($t$) as a function of the wealth Gap Index ($I_w$), the trust Index ($I_t$), and the oppression index ($I_o$):

$\displaystyle\frac{ dI_u }{ dt } = c_{uw} I_w + c_{ut} (1- I_t ) - c_{uo} I_o $

Conditions

Variables

Relation

Typical values of the wealth gap riots on the rise ($c_{uw}$), the reducing unrest through trust ($c_{ut}$), and the reduction of oppression riots ($c_{uo}$) are on the order of 0.07, 0.08, and 0.06 per year, respectively.

ID:(16144, 0)

Equation

>Top, >Model

The oppression index ($I_o$) varies with the time ($t$) as a function of the index of Unrest ($I_u$):

$\displaystyle\frac{ dI_o }{ dt } = c_{ou} I_u $

Conditions

Variables

Relation

Typical values of the increased oppression due to riots ($c_{ou}$) are on the order of 0.10 per year.

ID:(16145, 0)

Equation

>Top, >Model

The wealth Gap Index ($I_w$) varies with the time ($t$) as a function of the education Index ($I_e$) and the devaluation index ($I_c$) according to:

$\displaystyle\frac{ dI_w }{ dt } = c_{we} (1- I_e ) + c_{wc} I_c $

Conditions

Variables

Relation

Typical values of the widening wealth gap with economic power ($c_{wp}$) and the reducing the wealth gap through devaluation ($c_{wc}$) are on the order of 0.05 and 0.03 per year, respectively.

ID:(16146, 0)