# šBonding Curve

Last updated

Last updated

Since v2.4.0, Flap supports multiple bonding curves, but only one is active.

What is a Bonding Curve

Before listing on DEX, each token launched on flap is bonded to a bonding curve. When you buy tokens from the bonding curve, you send your ETH (or other quote token, usually the native token of that chain) to the bonding curve as a reserve, and the bonding curve mints tokens to your address. Or if you sell your tokens to the bonding curve, the bonding curve would burn your selling tokens and send the ETH back to you.

A bonding curve defines the relationship between the trading token's supply and the reserve (i.e. Quote tokens like ETH or BNB). The change of the reserve respect to the supply is the price. Our bonding curve is based on a constant product equation. You may have heard about this equation, which Uniswap popularized.

You may even wonder what is the difference between a bonding curve token launching platform like flap and Unsiwap? The answer is the liquidity. The liquidity does not change on the bonding curve. However, anyone can add liquidity to the Uniswap pools.

Flap's Bonding Curve-Alpha

Based on the above equation, we can get the reserve of the token from its circulating supply.

Bonding Curves On Different Chains

For different deployment, the value `r`

is different:

Let's take the latest BSC curve for example.

The `supply vs reserve`

graph is as follows:

When the circulating supply reaches 50% of the total supply, the reserve is 4 BNB.

When the circulating supply reaches 80% of the total supply, the reserve is 16 BNB.

On BSC chain, when the circulating supply reaches 80% of the total supply, the token will be listed on DEX. ( check List On DEX for more details ).

The token created on our platform has the max supply of $10^9$ , with 18 decimals. For each token, the remaining (non-circulating) supply of the token and the reserves (ETH or the native token of the target chain) follow the following constant product equation:

$x(y + r) = r \cdot 10^{9}$

$r$ is a constant parameter dependent on the target chain ( check Bonding Curves On Different Chains for more details).

$x(y + r) = r \cdot 10^{9}$

$x$ is the non circulating (either not minted or locked in Flap's contract) of the token, initially, it is $10^9$, which means all the tokens are not circulating in the beginning.

$y$ is the reserve of ETH , it is 0 in the beginning, which means all the liquidity are provided with the token then.

To better understand the bonding curve, we use $s$ to denote the token's current (circulating) supply. And the relationship between $s$ and $x$ is straightforward:

$x = 10^9 - s$

We can get the following relationship between $s$ and $y$ :

$(10^9 - s)(y + r) = r \cdot 10^{9}$

Chain | r |
---|---|

BSC (Legacy before block #42042177 )

15

BSC (latest since block 42042177)

4

1ETH

0.974