Dynamics of Coupled Adaptive Elements : Bursting and Intermittent Oscillations Generated by Frustration in Networks - Physics > Biological PhysicsReport as inadecuate




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Abstract: Adaptation to environmental change is a common property of biologicalsystems. Cells initially respond to external changes in the environment, butafter some time, they regain their original state. By considering an elementconsisting of two variables that show such adaptation dynamics, we studied acoupled dynamical system containing such elements to examine the diversedynamics in the system and classified the behaviors on the basis of the networkstructure that determined the interaction among elements. For a system with twoelements, two types of behaviors, perfect adaptation and simple oscillation,were observed. For a system with three elements, in addition to these twotypes, novel types of dynamics, namely, rapid burst-type oscillation and a slowcycle, were discovered; depending on the initial conditions, these novel typesof dynamics coexisted. These behaviors are a result of the characteristicdynamics of each element, i.e., fast response and slow adaptation processes.The behaviors depend on the network structure in specific, a combination ofpositive or negative feedback among elements. Cooperativity among elements dueto a positive feedback loop leads to simple oscillation, whereas frustrationinvolving alternating positive and negative interactions among elements leadsto the coexistence of rapid bursting oscillation and a slow cycle. Thesebehaviors are classified on the basis of the frustration indices defined by thenetwork structure. The period of the slow cycle is much longer than theoriginal adaptation time scale, while the burst-type oscillation is a continuedresponse that does not involve any adaptation. We briefly discuss the universalapplicability of our results to a network of a larger number of elements andtheir possible relevance to biological systems.



Author: Masayo Inoue, Kunihiko Kaneko

Source: https://arxiv.org/







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