# Modelling Patterns

## Pattern 1 – Single positive influence with positive direct feedback

The pattern consist of rate Rx and a state variable Sa. The mechanism consists of a direct influence (I+) from the rate on the state variable. The direct positive feedback is implemented using a proportionality (P+), from the state variable to the rate.

Details pattern 1.pdf

## Pattern 2 – Single positive influence with positive indirect feedback

The pattern consist of rate Rx, a state variable Sa, and two auxiliary quantities (Aa and Ab). The mechanism consists of a direct influence (I+) from the rate on the state variable. The indirect positive feedback is implemented using three proportionality statements (P+), namely from Sa to Aa, from Aa to Ab, and from Ab finally back to the rate.

Details pattern 2.pdf

## Pattern 3 – Single positive influence with negative direct feedback

The pattern consist of rate Rx and a state variable Sa. The mechanism consists of a direct influence (I+) from the rate on the state variable. The direct negative feedback is implemented using a proportionality (P-), from the state variable to the rate.

Details pattern 3.pdf

## Pattern 4 – Single positive influence with negative indirect feedback

The pattern consist of rate Rx, a state variable Sa, and two auxiliary quantities (Aa and Ab). The mechanism consists of a direct influence (I+) from the rate on the state variable. The indirect negative feedback is implemented using two positive proportionality statements and one negative, namely from Sa to Aa (P+), from Aa to Ab (P+), and from Ab finally back to the rate (P-).

Details pattern 4.pdf

## Pattern 5 – Single negative influence with positive direct feedback

The pattern consist of rate Rx and a state variable Sa. The mechanism consists of a negative direct influence (I-) from the rate on the state variable. The direct positive feedback is implemented using a proportionality (P+), from the state variable to the rate.

Details pattern 5.pdf

## Pattern 6 – Single negative influence with positive indirect feedback

The pattern consist of rate Rx, a state variable Sa, and two auxiliary quantities (Aa and Ab). The mechanism consists of a negative direct influence (I-) from the rate on the state variable. The indirect positive feedback is implemented using three proportionality statements (P+), namely from Sa to Aa, from Aa to Ab, and from Ab finally back to the rate.

Details pattern 6.pdf

## Pattern 7 – Single negative influence with negative direct feedback

The pattern consist of rate Rx and a state variable Sa. The mechanism consists of a negative direct influence (I-) from the rate on the state variable. The direct negative feedback is implemented using a proportionality (P-), from the state variable to the rate.

Details pattern 7.pdf

## Pattern 8 – Single negative influence with negative indirect feedback

The pattern consist of rate Rx, a state variable Sa, and two auxiliary quantities (Aa and Ab). The mechanism consists of a negative direct influence (I-) from the rate on the state variable. The indirect negative feedback is implemented using two positive proportionality statements and one negative, namely from Sa to Aa (P+), from Aa to Ab (P+), and from Ab finally back to the rate (P-).

Details pattern 8.pdf

## Pattern 9 – Mixed influence with direct negative feedback – Equilibrium

The pattern has one rate (Rx) and two state variables (Sa and Sb). The mechanism implements a balance. With unequal state variables the rate will produce a rate that decreases the higher quantity (I-) and increases the lower quantity (I+). The magnitude of the rate is determined by the differences in the magnitudes of the state variables (Sa-Sb=Rx). The rate changes due to feedback from the state variables, which are both direct and negative with respect to the rate (P+ and P-, respectively).

Details pattern 9.pdf

## Pattern 10 – Mixed influence with indirect negative feedback – Equilibrium

The pattern has one rate (Rx) and two state variables (Sa and Sb). The mechanism implements a balance. With unequal state variables the rate will produce a rate that decreases the higher quantity (I-) and increases the lower quantity (I+). The magnitude of the rate is determined by the differences in the magnitudes of the state variables (Sa-Sb=Rx). The rate changes due to feedback from the state variables, which is negative and indirect. It goes via Sa to Ab, from Ab to Aa, and from Aa back to the Rx, and via Sb to Ac, from Ac to Ad, and from Ad back to the Rx.

Details pattern 10.pdf

## Pattern 11 – Mixed influence with mixed direct feedback – Competing

The pattern has two rates (Rx and Ry) and one state variable Sa. The mechanism consists of two parts, a positive (I+) and a negative one (I-). The negative part has a direct negative feedback (P+), while the positive part has a direct positive feedback. Depending on the relative magnitudes of the rates, the state variable will increase (positive effect bigger), become or stay in balance (equally strong), or decrease (negative effect bigger).

Details pattern 11.pdf

## Pattern 12 – Mixed influence with mixed indirect feedback – Competing

The pattern has two rates (Rx and Ry) and one state variable Sa. The mechanism consists of two parts, a positive (I+) and a negative one (I-). The negative part has an indirect negative feedback, while the positive part has an indirect positive feedback. Depending on the relative magnitudes of the rates, the state variable will increase (positive effect bigger), become or stay in balance (equally strong), or decrease (negative effect bigger).

Details pattern 12.pdf 