In the real world, both the MCAP and the TVL can fluctuate due to a variety of factors including market dynamics, changes in the network, and user behavior. Therefore, it's reasonable to model the staking ratio as a time-dependent function with fluctuations.
Where:
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The model represents the token demand for staking in the network. Staking is a process where holders of a cryptocurrency participate in the network by locking or "staking" their tokens in a wallets or other constructions (i.e., smart contract) to support the operations of a blockchain network, such as transaction validation, security, and governance. These participants are rewarded for staking their coins, thereby incentivizing this activity.
In the model, is calculated as the cumulative token supply divided by a staking ratio (). The staking ratio is a time-dependent function, initially set high and then decreasing over time. This decreasing trend is overlaid with stochastic oscillations to represent the fluctuations in staking behavior over time.
The function used here is a proxy for the metric. MCAP stands for Market Capitalization, which is the total value of all the tokens in circulation. TVL (Total Value Locked) is a metric often used in DeFi (Decentralized Finance) to measure the amount of crypto assets that are currently staked or locked in a specific protocol or platform.
As a ratio, reflects the relationship between the total value of the tokens and the amount of those tokens currently being staked or used in applications. This ratio can give insights into the overall health and participation of users in a network.
To sum up, is a modelled approximation of the token demand for staking, based on the cumulative token supply and a staking ratio that reflects real-world metrics and behaviors.
o is the cumulative amount of tokens available to the network
o is staking ratio
o is mantissa of staking ratio
o are fluctuations.
