Chaos最新文献 - Book学术

Self-organizing network representation of human heart.

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0243391

Runsang Liu, Hui Yang

引用次数: 0

Adaptive network approach to exploration-exploitation trade-off in reinforcement learning.

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0221833

Mohammadamin Moradi, Zheng-Meng Zhai, Shirin Panahi, Ying-Cheng Lai

{"title":"Adaptive network approach to exploration-exploitation trade-off in reinforcement learning.","authors":"Mohammadamin Moradi, Zheng-Meng Zhai, Shirin Panahi, Ying-Cheng Lai","doi":"10.1063/5.0221833","DOIUrl":"https://doi.org/10.1063/5.0221833","url":null,"abstract":"A foundational machine-learning architecture is reinforcement learning, where an outstanding problem is achieving an optimal balance between exploration and exploitation. Specifically, exploration enables the agents to discover optimal policies in unknown domains of the environment for gaining potentially large future rewards, while exploitation relies on the already acquired knowledge to maximize the immediate rewards. We articulate an approach to this problem, treating the dynamical process of reinforcement learning as a Markov decision process that can be modeled as a nondeterministic finite automaton and defining a subset of states in the automaton to represent the preference for exploring unknown domains of the environment. Exploration is prioritized by assigning higher transition probabilities to these states. We derive a mathematical framework to systematically balance exploration and exploitation by formulating it as a mixed integer programming (MIP) problem to optimize the agent's actions and maximize the discovery of novel preferential states. Solving the MIP problem provides a trade-off point between exploiting known states and exploring unexplored regions. We validate the framework computationally with a benchmark system and argue that the articulated automaton is effectively an adaptive network with a time-varying connection matrix, where the states in the automaton are nodes and the transitions among the states represent the edges. The network is adaptive because the transition probabilities evolve over time. The established connection between the adaptive automaton arising from reinforcement learning and the adaptive network opens the door to applying theories of complex dynamical networks to address frontier problems in machine learning and artificial intelligence.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Arnold tongues, shrimp structures, multistability, and ecological paradoxes in a discrete-time predator-prey system.

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0230994

Rajni, Bapan Ghosh

{"title":"Arnold tongues, shrimp structures, multistability, and ecological paradoxes in a discrete-time predator-prey system.","authors":"Rajni, Bapan Ghosh","doi":"10.1063/5.0230994","DOIUrl":"https://doi.org/10.1063/5.0230994","url":null,"abstract":"This paper explores a discrete-time system derived from the well-known continuous-time Rosenzweig-MacArthur model using the piecewise constant argument. Examining the impact of increasing carrying capacity and harvesting efforts, we uncover intricate phenomena, such as periodicity, quasiperiodicity, period-doubling, period-bubbling, and chaos. Our analysis reveals that increasing the carrying capacity of prey species can lead to both system stabilization and destabilization. We delve into normal forms associated with different bifurcation types, accompanied by numerical examples, observing multistabilities with intricate basin structures. Bistable, tristable, and quadruple attractors characterize the model's multistable states. Additionally, we find that enriching prey species negatively affects predator abundance, and increasing carrying capacity can lead to a sudden jump in predator population to the brink of extinction. Examining the two-parameter space of predator and prey harvesting efforts, we identify organized periodic structures: Arnold tongues and shrimp-like structures within quasiperiodic and chaotic regions. Arnold tongues exhibit a sequence of periodic adding. The shrimp structures indicate the existence of period-doubling and period-bubbling phenomena. Discussions on ecological interpretations of predator harvesting, including the paradoxical hydra effect, are provided.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stern-Brocot arithmetic in dynamics of a biochemical reaction model.

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0231719

Lars Folke Olsen

引用次数: 0

Strange nonchaotic attractor in an unforced turbulent reactive flow system.

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0233819

Beeraiah Thonti, Shruti Tandon, Premraj Durairaj, R I Sujith

引用次数: 0

Evolution of cooperation with early social influence for explaining collective action.