Severity: Warning
Message: fopen(/var/lib/php/sessions/ci_session6dp2tmu6tk82j9p2rh9ledrmshsa26f7): Failed to open stream: No space left on device
Filename: drivers/Session_files_driver.php
Line Number: 177
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File: /var/www/html/index.php
Line: 316
Function: require_once
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Filename: Session/Session.php
Line Number: 137
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File: /var/www/html/index.php
Line: 316
Function: require_once
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Message: Undefined array key "choices"
Filename: controllers/Detail.php
Line Number: 249
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File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated
Filename: models/Detail_model.php
Line Number: 71
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File: /var/www/html/application/models/Detail_model.php
Line: 71
Function: strpos
File: /var/www/html/application/controllers/Detail.php
Line: 252
Function: insertAPISummary
File: /var/www/html/index.php
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Function: require_once
Severity: 8192
Message: str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated
Filename: helpers/my_audit_helper.php
Line Number: 8919
Backtrace:
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 8919
Function: str_replace
File: /var/www/html/application/controllers/Detail.php
Line: 255
Function: formatAIDetailSummary
File: /var/www/html/index.php
Line: 316
Function: require_once
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Message: Undefined array key "choices"
Filename: controllers/Detail.php
Line Number: 256
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 256
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 256
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Undefined array key "usage"
Filename: controllers/Detail.php
Line Number: 257
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 257
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Undefined array key "usage"
Filename: controllers/Detail.php
Line Number: 258
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 258
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 258
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 258
Function: _error_handler
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: Undefined array key "usage"
Filename: controllers/Detail.php
Line Number: 259
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File: /var/www/html/application/controllers/Detail.php
Line: 259
Function: _error_handler
File: /var/www/html/index.php
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
Line: 259
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Undefined array key "usage"
Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
Line: 260
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
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Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
Line: 260
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: file_get_contents(https://...@gmail.com&api_key=61f08fa0b96a73de8c900d749fcb997acc09): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests
Filename: helpers/my_audit_helper.php
Line Number: 143
Backtrace:
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 143
Function: file_get_contents
File: /var/www/html/application/helpers/my_audit_helper.php
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Function: simplexml_load_file_from_url
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3098
Function: getPubMedXML
File: /var/www/html/application/controllers/Detail.php
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Function: pubMedSearch_Global
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Function: pubMedGetRelatedKeyword
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Message: Attempt to read property "Count" on bool
Filename: helpers/my_audit_helper.php
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File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3100
Function: _error_handler
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File: /var/www/html/application/controllers/Detail.php
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Function: pubMedGetRelatedKeyword
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Function: require_once
We apply the horizontal visibility to study the class of unimodal maps that give rise to equivalent bifurcation diagrams. We use the classical logistic map to illustrate the main results of this paper: there are visibility patterns in each cascade of the bifurcation diagram, converging at the onset of chaos. The visibility pattern of a periodic time series is generated from elementary blocks of visibility in a recursive way. This rule of recurrence applies to all periodic-doubling cascades. Within a particular window, as the growth parameter r varies and each period doubles, these blocks are recurrently embedded, forming the visibility pattern for each period. In the limit, at the onset of chaos, an infinite pattern of visibility appears, containing all visibility patterns of the periodic time series of the cascade. We have seen that these visibility patterns have specific properties: (i) the size of the elementary blocks depends on the period of the time series, (ii) certain time series sharing the same periodicity can have different elementary blocks and, therefore, different visibility patterns, and (iii) since the 2-period and 3-period windows are unique, the respective elementary blocks, {2} and {23}, are also unique and thus their visibility patterns. We explore the visibility patterns of other low-periodic time series and also enumerate all elementary blocks of each of their periodic windows. All of these visibility patterns are reflected in the corresponding accumulation points at the onset of chaos, where periodicity is lost. Finally, we discuss the application of these results in the field of non-linear dynamics.
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Source |
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http://dx.doi.org/10.1063/5.0006652 | DOI Listing |
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