Resilience; Stability Landscape

A stability landscape is multidimensional state space and represents all possible state variables in a system (Walker et.al 2004). Within this state space lie attractors of many sizes and shapes representing different stability characteristics. In the case of equilibrium attractors these locations are known as basin of attraction (3 dimensional state space) corresponding to qualitatively quasi-stable states a system may inhibit. The size and shape of the basin of attraction indicates the resilience of the corresponding state and its ability to withstand disturbances and adapt to main maximum performance with resilience threshold. The state space is dynamic therefore its topography is continuously fluctuating (changes in parameters and variables) which may affect the coordinates of the basin threshold (location and height). When perturbed a system may escape the attractor, cross the threshold and reach alternate state (new regime) which results in a functional change and a different set of controlling processes and performance capacity. The state space within a stability landscape may not be continuous as windows of opportunity or disaster may open or close (new basin of attraction) and some alternate states may not be directly reachable from current state of the system.

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Industry paradigm which represents a window of opportunity that opens a new basin of attraction within it stability landscape and at the same time influences other stability landscapes by triggering perturbation (new industry paradigm may causes a crumbling paradigm).

Resilience stability landscape contains multiple possible regimes with its equilibrium, resilience, tipping points and contains possible pathway (good or bad) depending on the efficacy of adaptation. The associated regimes are not endless; tipping points can lead to nothingness (extinction). The basin of attraction are also influenced by external conditions related other system; example an economic system of a country stability landscape is influenced by another country stability landscape and other factors. An organization that creates new industrial paradigm will influence the stability landscape of its competitor. Resilience and therefore stability landscape topography is dependent not solely on system configuration but also on the perturbations of interest. Regime shifts (a what to what) that result from movement of a system from one basin to another are dependent on the type, magnitude an timing of perturbations as well as the cumulative effects of multiple disturbances and the rate system recovery (Scheffer at all.2001 Folke et al.2014).

The landscape can be influenced internally (management abilities, historical resilience behavior, systemic potential) and externally conditions (environment, business competition).

Changes in the stability landscape may result in a contraction of the basin the system was in and expansion of the alternate basin. These changes are influenced by exogenous drivers; where a new industry paradigm based on innovation and or transformation of one organization can influence stability landscape of the system.

Mechanisms driving resilience shifts can be depicted using “stability landscapes”: valleys represent stability domains, or basins of attraction, in which a system, represented by the ball, in (BASIN A) is kept by internal feedback mechanisms in equilibrium (fig a) cumulative changes in system variables can lead to a gradual loss of resilience, here represented by changes in the depth of the valley (fig b Basin A) that becomes shallower up to a point where even a small disturbance can push the system into a new basin of attraction, under a different threshold; (fig b Basin A to Basin B ) an intense shock can also push the system into a new resilience threshold (fig c Basin D to Basin E).

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When a system shifts into a new reliance threshold, it reaches and is kept in a new state by internal feedback dynamics characteristic of that resilience threshold (Basin B or Basin Eas). This makes the recovery to the previous regime very difficult, especially when lag effects in the system’s response hinder its recovery.

In some cases resilience threshold shifts are mediated by tipping points , that is, a non-linear evolution of the system, where an additional small change causes the passing of a threshold and leads to an abrupt change (relatively to the baseline system dynamics). These tipping-point dynamics result from reinforcing feedbacks that amplify the impacts of the drivers of change.

 

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