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What is a bonding curve?

Before migration to 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: BNB, OKB, USD1 etc ) 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. 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 is popularized by Uniswap. Effectively, our bonding curve defines a concentrated liquidity range similar to the range between two fixed tickers in Uniswap V3.

You may wonder what is the difference between a bonding curve token launching platform 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

The token launched on Flap Protocol has the same max supply of $10^9$ , with 18 decimals. For each token, the amount of base token (i.e the launched meme token) and the quote token (i.e the token as the reserve: ETH, BNB, OKB etc) follow the following constant product equation:

$$(x+ h)(y + r) = K$$

$r$ ,$h$ and $K$ are immutable bonding curve parameters for each launched token. Note that the parameters for each token may be different. It is better to assume that each token launched from Flap Protocol has different curve parameters.

$$(x+ h)(y + r) = K$$

• $x$ is the amount of base token in the bonding curve, initially, it is $10^9$, which means all the tokens are still in the bonding curve.

• $y$ is the amount of quote token , it is 0 in the beginning.

• Our curve have 3 constant parameters:

  • $r$ can be interpreted as the virtual reserve of quote token (ETH, BNB, OKB etc) in the bonding curve

  • $h$ can be interpreted as the virtual reserve of base token in the bonding curve

  • $K$ is the square of the virtual liquidity

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