Nice question dear Mohammad, during the process of ecological succession the stage called stability in which the diversity of that particular region gets stabilize after that there is the competition between species for various aspects.
whereas sustainability is the utilization of resource without compromising the other, or the future generation.
there are several articles avail online, hope which will help you for your further studies.
Stability can be a feature of a sustainable system but is not necessarily. While stability is a way to characterize system behavior (often with one, sometimes more variables), and is quite well bounded to certain methods in dynamic system analysis, sustainability is a broader normative term. In order to be meaningful, sustainability has also to be linked to time scale and a set of important response variables (at least 2, often more). With the 'importance' the normative notion steps in: People define what values they want to preserve, from the environmental, economic or social sector. They can for example define instability as a valuable feature of other states so that their own economy 'sustainably' flourishs. So, for both terms it is always important to ask 'of what?' and 'for how long?'. Finally, the context of these terms is quite different: While stability is analysed in quite confined systems, sustainability can hardly be used as solely ecological feature without considering human perception and impact.
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Sustainability, how I know it, is a situation which the current generation's needs are provided without any risk being posed on the following generation's needs.Therefore sustainability can be perceived as a factor of stability. I feel that stability is more difficult to define considering that there is no strict definition that is universally agreed upon. There are several concepts and mechanisms that are included in the topic of stability such as the interactions between the species of organisms within the environment and the way in which the species experience disturbances to the environment, whether natural or man-made.