In order to conserve natural resources, the quest for recycling water and food waste culture is ongoing. One of the possible and good ways to reuse these wastes is hydroponic culture. It is an advanced technology that cultivates plants without soil. Instead of using root system, it needs nutrient-rich water. Most of the nutrients used in hydroponic culture come from aqua culture, the branch for propagation, emergence, and maintenance of aquatic (water) organisms. Humans convolve aqua culture with hydroponic culture that has come up as an aquaponic system. It has been universally adopted for indoor food production. The solution arising out of this system has eliminated the lack of vegetable and fish. The continuous nature of these cultures gives rise to the system of non-linear ordinary differential equations. This system is investigated through logistic growth rate. Logistic growth rate offers an oscillating threshold. The simulative results analyse the periodicity of the system solutions, which will help the ecosystem survive.
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People need water and food the most in order to live. Most of them are not item that people use and they last for a long time or an eternity. The item that is no longer useful is called waste. But in this innovative human world, we may convert waste into its by-products, composite products or resources. This is an experimental way to increase the value of waste from zero. Moreover, humans are constantly searching the various ways to recycle waste in reusable products. In this study, waste water and food have been targeted for vegetable production and fish preservation.
Any water that has been affected by human use can be classified as waste water. Waste water is water sourced from the combination of domestic, industrial, commercial or agricultural activities. Therefore, waste water can be bifurcated into domestic water, industrial water, commercial water and agricultural water. Among these waste waters, industrial waste water is the most difficult type to recycle. Vacuum process helps to effectively treat industrial waste water which sometime lead to a system with zero discharge. This technology has many profits like it is hygienic, secure, versatile and has low management cost. Moreover, it is one of the most adequate and efficient techniques for treating aqueous effluents. Treated water uses in branch of algae culture. Algae culture involves the plants grow in water resource.
Waste food reflects the food that has been used by living creature. The word “waste food” is either wasted, lost or uneaten food whose disposal is the global problem. It can be biodegraded using fly/worm in order to make feed for fishes. Fish is the creature lives in aqua culture, a branch of propagating, rising and keeping of aquatic organisms.
Algae culture and aqua culture are closely related. They contain definite level of uneaten nutrients. These nutrients are excreted by fish and algae which supplies to hydroponic culture. Hydroponics is a method of growing plants in water based, nutrient rich solution not on the growing using soil on the land. In this method, the root system is supported using an inert medium such as perlite, rockwool, clay pellets, peat moss, or vermiculite. The key purpose behind hydroponics is to allow the plants roots to come in direct contact with the nutrients, while also having access to oxygen, which is essential for proper growth. When aqua culture convolves with hydroponic culture then one branch is emerged that is called aquaponics. In this system, the toxic water accumulates from aqua culture that is fed to hydroponic system and the by-products are broken down by nitrifying bacteria initially into nitrites and subsequently into nitrates that are utilized by the plants as nutrients. Then, the water is recirculated back to the aquaculture system. In this way, the aquaponic system results in the production of vegetables and the preservation of fish which is very fruitful for the human society.
Aquaponic system is emerging concept for research world. Diver and Rinehart (2000) have studied the branch of Aquaponics in which hydroponics integrated with aquaculture. Extended study was done through Chen et al. (2018) using breakthrough technologies for the biorefining of organic solid and liquid wastes. Mathematical Modeling has been done for waste water and food from various researchers. Xiang et al. (2013) prepared dynamic modeling and simulation of water environment management with a focus on water recycling. The concept of mathematical modeling for water usage and treatment network design is used by Huang et al. (1999). Similarly, for residential food generation, Benitez et al. (2008) have developed a mathematical model.
The objective of this chapter is to revive agriculture and aquatic balance. In section 2, a mathematical model for aquaponic system using sinusoidal periodic function is developed along with its equilibrium points and threshold. The global stability analysis is derived in section 3. Section 4 represents the numerical simulation to validate our results with parametric data.