About this Research Topic
Stability of equilibrium paths and of the evolution of dynamical systems is a classic field which has broad implication in virtually any field of science, from physics to human sciences and ubiquitous applications from engineering to economics. Stability plays also an important role in the theory of differentiable mappings and more generally in the classification of geometrical objects.
However, there is no absolute definition of stability and this concept has constantly evolved and has been adjusted to the special requirements of particular problems in different fields. From a methodological standpoint, investigations in stability have seen a progressive shift from analytical to differential-topological methods and numerical procedures have gained a significant role.
In mathematics, it is generally accepted that stability theory investigates the variation of the phase portrait of a dynamical system under small variations of the system itself by means of diffeomorphisms, or the variation of the global properties of a differentiable map between two manifolds, by means of diffeomorphisms – or homeomorphisms – on the manifolds.
Noticeably, even stability of structures, has been, and remains to a certain extent, an old conundrum proven by the consistent disagreement between theoretical and experimental results. Over the past century, this required the introduction of various knockdown factors based on deterministic or probabilistic approaches.
The same applies to the stability of ergodic systems, whose stochastic treatment of initial parameters has often proved inaccurate in predicting their evolution. All these systems are affected by small perturbations and it has been believed that an approach based on appropriate statistical information could lead to a rational prediction of their behaviour and evolution.
Therefore, even if at first sight this topic might seem a much investigated one, it is felt that much remains to be discussed with respect to specific aspects and that collecting the views of several scholars from different areas could help to bring together the most update experiences and focus the state of the art in a fundamentally interdisciplinary field.
In this Research Topic, we welcome contributions from areas ranging from mathematical physics and engineering to economics, biology, chemistry and social sciences which can highlight the role of stability in static or evolutionary systems. Ideally, contributions should make reference to examples and systems which can be understood by a broad audience of scholars and allow the dissemination of the results in a multidisciplinary framework.
However, there is no absolute definition of stability and this concept has constantly evolved and has been adjusted to the special requirements of particular problems in different fields. From a methodological standpoint, investigations in stability have seen a progressive shift from analytical to differential-topological methods and numerical procedures have gained a significant role.
In mathematics, it is generally accepted that stability theory investigates the variation of the phase portrait of a dynamical system under small variations of the system itself by means of diffeomorphisms, or the variation of the global properties of a differentiable map between two manifolds, by means of diffeomorphisms – or homeomorphisms – on the manifolds.
Noticeably, even stability of structures, has been, and remains to a certain extent, an old conundrum proven by the consistent disagreement between theoretical and experimental results. Over the past century, this required the introduction of various knockdown factors based on deterministic or probabilistic approaches.
The same applies to the stability of ergodic systems, whose stochastic treatment of initial parameters has often proved inaccurate in predicting their evolution. All these systems are affected by small perturbations and it has been believed that an approach based on appropriate statistical information could lead to a rational prediction of their behaviour and evolution.
Therefore, even if at first sight this topic might seem a much investigated one, it is felt that much remains to be discussed with respect to specific aspects and that collecting the views of several scholars from different areas could help to bring together the most update experiences and focus the state of the art in a fundamentally interdisciplinary field.
In this Research Topic, we welcome contributions from areas ranging from mathematical physics and engineering to economics, biology, chemistry and social sciences which can highlight the role of stability in static or evolutionary systems. Ideally, contributions should make reference to examples and systems which can be understood by a broad audience of scholars and allow the dissemination of the results in a multidisciplinary framework.
Keywords: Stability, complex systems, uncertainty, numerical, probabilistic approach
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