It is well known that there exists a large class of systems whose states are always nonnegative in the real world, for example, biological systems, chemical process, economic systems, and so on.
Potential mechanisms for the physical activity- mental health relationship are, for example, biological systems (such as serotonin) and psychological and psychosocial factors (such as improved self-esteem, self-efficacy, perceived behavioral control or cognitive functioning) [ 15- 18].
These data are revealing striking results, suggesting, for example, that biological systems are tuned to criticality, and that effective models of these systems based on only pairwise interactions among constitutive components provide surprisingly good fits to the data.
Particularly, measurements of the longitudinal relaxation time (T_{1}) (the decay lifetime for NVs population initialized to a ground-state magnetic sublevel) might result in development of new techniques to use NV− (T_{1}) as a spin probe, for example, in biological systems [18 24].
Even if we focused here on the integration of the simulation/analysis phases we demonstrate its efficiency and effectiveness by modeling three simple but paradigmatic examples of biological systems which are representative of different system dynamics, that is, multistable and oscillatory.
While there are examples of biological systems that exhibit synchronous dynamical patterns [ 42, 43], asynchronous simulations might be able to predict a wider range of biological behaviors.
Other examples of biological systems in which the effect of feedback and time delay were extensively studied can be found in the developmental regulator Hes1, which inhibits its own transcription [ 12, 13] or in the NFB loops in the p53 response [ 14, 15].
However, in real world problems, the impulses of many systems do not occur at fixed times [38], for example, biological and physiological systems including artificial neural networks, saving rates control systems, and some circuit control systems.
The convexity of functions plays a significant role in many fields, for example, in biological system, economy, optimization, and so on [3 5].
The convexity of functions is an important concept in the class mathematical analysis course, and it plays a significant role in many fields, for example, in biological system, economy, optimization, and so on [1 7].
Another example to control biological systems is also presented to show the feasibility of the proposed method.
