scholarly journals Emergence of Hidden Attractors through the Rupture of Heteroclinic-Like Orbits of Switched Systems with Self-Excited Attractors

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
R. J. Escalante-González ◽  
Eric Campos
Keyword(s):  
Switched Systems ◽  
Piecewise Linear ◽  
The Self ◽  
Heteroclinic Orbits ◽  
Bistable System ◽  
Necessary Condition ◽  
Hidden Attractor ◽  
Hidden Attractors

This work is dedicated to the study of an approach that allows the generation of hidden attractors based on a class of piecewise-linear (PWL) systems. The systems produced with the approach present the coexistence of self-excited attractors and hidden attractors such that hidden attractors surround the self-excited attractors. The first part of the approach consists of the generation of self-excited attractors based on pairs of equilibria with heteroclinic orbits. Then, additional equilibria are added to the system to obtain a bistable system with a second self-excited attractor with the same characteristics. It is conjectured that a necessary condition for the existence of the hidden attractor in this class of systems is the rupture of the trajectories that resemble heteroclinic orbits that join the two regions of space that surround the pairs of equilibria; these regions resemble equilibria when seen on a larger scale. With the appearance of a hidden attractor, the system presents a multistable behavior with hidden and self-excited attractors.

scholarly journals Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
R. J. Escalante-González ◽  
Eric Campos
Keyword(s):  
Vector Field ◽  
Linear Systems ◽  
Piecewise Linear ◽  
Hidden Attractor ◽  
Hidden Attractors ◽  
Key Space ◽  
Potential Applications ◽  
Current Design ◽  
Multistable Systems ◽  
Number Of Equilibria

In this work, we present an approach to design a multistable system with one-directional (1D), two-directional (2D), and three-directional (3D) hidden multiscroll attractor by defining a vector field on ℝ3 with an even number of equilibria. The design of multistable systems with hidden attractors remains a challenging task. Current design approaches are not as flexible as those that focus on self-excited attractors. To facilitate a design of hidden multiscroll attractors, we propose an approach that is based on the existence of self-excited double-scroll attractors and switching surfaces whose relationship with the local manifolds associated to the equilibria lead to the appearance of the hidden attractor. The multistable systems produced by the approach could be explored for potential applications in cryptography, since the number of attractors can be increased by design in multiple directions while preserving the hidden attractor allowing a bigger key space.

scholarly journals Agency and the Successive Structure of Time-Consciousness

Erkenntnis ◽  
2021 ◽  
Author(s):  
Camden Alexander McKenna
Keyword(s):  
Temporal Structure ◽  
Basic Structure ◽  
The Self ◽  
Necessary Condition ◽  
Epistemic Status ◽  
Mental Attitude ◽  
Time Consciousness ◽  
Possibility Space ◽  
The Right ◽  
Wrong Sort

AbstractI argue for constraining the nomological possibility space of temporal experiences and endorsing the Succession Requirement for agents. The Succession Requirement holds that the basic structure of temporal experience must be successive for agentive subjects, at least in worlds that are law-like in the same way as ours. I aim to establish the Succession Requirement by showing non-successively experiencing agents are not possible for three main reasons, namely that they (1) fail to stand in the right sort of causal relationship to the outcomes of their actions, (2) exhibit the wrong sort of epistemic status for agency, and (3) lack the requisite agentive mental attitude of intentionality. I conclude that agency is incompatible with non-successive experience and therefore we should view the successive temporal structure of experience as a necessary condition for agency. I also suggest that the Succession Requirement may actually extend beyond my main focus on agency, offering preliminary considerations in favor of seeing successive experience as a precondition for selfhood as well. The consequences of the Succession Requirement are wide-ranging, and I discuss various implications for our understanding of agency, the self, time consciousness, and theology, among other things.

A SUFFICIENT AND NECESSARY CONDITION FOR CREDIBILITY MEASURES

2006 ◽  
Vol 14 (05) ◽  
pp. 527-535 ◽  
Author(s):  
XIANG LI ◽  
BAODING LIU
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Extension Theorem ◽  
The Self ◽  
Necessary Condition ◽  
Self Duality ◽  
Duality Property ◽  
Sufficient And Necessary Condition

Possibility measures and credibility measures are widely used in fuzzy set theory. Compared with possibility measures, the advantage of credibility measures is the self-duality property. This paper gives a relation between possibility measures and credibility measures, and proves a sufficient and necessary condition for credibility measures. Finally, the credibility extension theorem is shown.

scholarly journals Detection of biological switches using the method of Gröebner bases

2019 ◽  
Vol 20 (1) ◽  
Author(s):  
Yaman Arkun
Keyword(s):  
Protein Kinase ◽  
Gaussian Elimination ◽  
Mitogen Activated Protein Kinase ◽  
Bistable System ◽  
Necessary Condition ◽  
Stable Steady State ◽  
Groebner Bases ◽  
Stable States ◽  
State Variable ◽  
Mitogen Activated Protein

Abstract Background Bistability and ability to switch between two stable states is the hallmark of cellular responses. Cellular signaling pathways often contain bistable switches that regulate the transmission of the extracellular information to the nucleus where important biological functions are executed. Results In this work we show how the method of Gröebner bases can be used to detect bistability and output switchability. The method of Gröebner bases can be seen as a multivariate, non-linear generalization of the Gaussian elimination for linear systems which conveniently seperates the variables and drastically simplifies the simultaneous solution of polynomial equations. A necessary condition for fixed-point state bistability is for the Gröbner basis to have three distinct solutions for the state. A sufficient condition is provided by the eigenvalues of the local Jacobians. We also introduce the concept of output switchability which is defined as the ability of an output of a bistable system to switch between two different stable steady-state values. It is shown that bistability does not necessarily guarantee switchability of every state variable of the system. We further show that, for a bistable system, the necessary conditions for output switchability can be derived using the Gröebner basis. The theoretical results are incorporated into an analysis procedure and applied to several systems including the AKT (Protein kinase B), RAS (Rat Sarcoma) and MAPK (Mitogen-activated protein kinase) signal transduction pathways. Results demonstrate that the Gröebner bases can be conveniently used to analyze biological switches by simultaneously detecting bistability and output switchability. Conclusion The Gröebner bases provides a novel methodology to analyze bistability. Results clarify the distinction between bistability and output switchability which is lacking in the literature. We have shown that theoretically, it is possible to have an output subspace of an n-dimensional bistable system where certain variables cannot switch. It is possible to construct such systems as we have done with two reaction networks.

scholarly journals HIDDEN ATTRACTORS IN DYNAMICAL SYSTEMS. FROM HIDDEN OSCILLATIONS IN HILBERT–KOLMOGOROV, AIZERMAN, AND KALMAN PROBLEMS TO HIDDEN CHAOTIC ATTRACTOR IN CHUA CIRCUITS

2013 ◽  
Vol 23 (01) ◽  
pp. 1330002 ◽  
Author(s):  
G. A. LEONOV ◽  
N. V. KUZNETSOV
Keyword(s):  
Dynamical Systems ◽  
Numerical Methods ◽  
Automatic Control ◽  
Control Systems ◽  
Computational Procedure ◽  
Phase Locked Loops ◽  
Hidden Attractor ◽  
Hidden Attractors ◽  
Computational Point ◽  
Hidden Oscillations

From a computational point of view, in nonlinear dynamical systems, attractors can be regarded as self-excited and hidden attractors. Self-excited attractors can be localized numerically by a standard computational procedure, in which after a transient process a trajectory, starting from a point of unstable manifold in a neighborhood of equilibrium, reaches a state of oscillation, therefore one can easily identify it. In contrast, for a hidden attractor, a basin of attraction does not intersect with small neighborhoods of equilibria. While classical attractors are self-excited, attractors can therefore be obtained numerically by the standard computational procedure. For localization of hidden attractors it is necessary to develop special procedures, since there are no similar transient processes leading to such attractors. At first, the problem of investigating hidden oscillations arose in the second part of Hilbert's 16th problem (1900). The first nontrivial results were obtained in Bautin's works, which were devoted to constructing nested limit cycles in quadratic systems, that showed the necessity of studying hidden oscillations for solving this problem. Later, the problem of analyzing hidden oscillations arose from engineering problems in automatic control. In the 50–60s of the last century, the investigations of widely known Markus–Yamabe's, Aizerman's, and Kalman's conjectures on absolute stability have led to the finding of hidden oscillations in automatic control systems with a unique stable stationary point. In 1961, Gubar revealed a gap in Kapranov's work on phase locked-loops (PLL) and showed the possibility of the existence of hidden oscillations in PLL. At the end of the last century, the difficulties in analyzing hidden oscillations arose in simulations of drilling systems and aircraft's control systems (anti-windup) which caused crashes. Further investigations on hidden oscillations were greatly encouraged by the present authors' discovery, in 2010 (for the first time), of chaotic hidden attractor in Chua's circuit. This survey is dedicated to efficient analytical–numerical methods for the study of hidden oscillations. Here, an attempt is made to reflect the current trends in the synthesis of analytical and numerical methods.

scholarly journals Science, Objectivity and Ethics in Research Methodology

1998 ◽  
Vol 15 (1) ◽  
pp. 113-126
Author(s):  
Nasr Arif
Keyword(s):  
Ways Of Knowing ◽  
Point Of View ◽  
The Self ◽  
Necessary Condition ◽  
Abuse Of Power ◽  
Operational Intelligence ◽  
Partial Truth ◽  
Ethics In Research ◽  
Correct Application ◽  
Selection Of

Islam recognizes that Truth is infinite and that different methods arenecessary to reach its different aspects. In other words, in the Islamic paradigm,each methodology has its appropriate domain which admits thepossibility of certitude while allowing for openness. Clearly, this is thepolar opposite of the relativist who claims that no method can reachTruth, he denies certitude and dogmatically insists that there is no suchthing as Truth. However, the self-contradictory nahm of the assertionproves it is false.’From the Islamic point of view, no single methodology can make aclaim on all knowledge contained in all fields and at all levels. This isreflected in the traditional formula inserted at the end of scholarly matiseswu’lluhu u’lum “God knows best,” for no scholar can claim to havecome to the end of knowledge, thereby encompassing the infinite Truthin a self-contained system of thought.The Islamic approach to knowledge refuses to accept partial truth as ifit were the whole, and a single methodology as if it were the onlymethodology. Objectivity requires recognizing a partial truth for what itis, and not making monopolistic claims on knowledge with a singlemethodology. This recognition limits the abuse of power by those whowould deny other valid methodologies and “ways of knowing.’”Recognizing the multiplicity of methods requires discernment as totheir correct application in specific domains. This requires wisdom and afully operational intelligence unobscured by passion. In other words, theintelligence or ‘uql must be wholesome4e ethics and justice of theresearcher being a necessary condition for discerning appropriatemethodologies. Muslim scholars, therefore, emphasize the ethical trainingof the scientist to ensure the just selection of methodologies in eachdomain ...

scholarly journals Heidegger’s Struggle with History

2021 ◽  
pp. 61
Author(s):  
Ingo Farin
Keyword(s):  
Life Time ◽  
Frankfurt School ◽  
The Self ◽  
Necessary Condition ◽  
The Real ◽  
Historical Reality ◽  
Human Intentionality ◽  
Time Frames ◽  
Intentional Acts

In this paper I analyze early Heidegger’s concept of history. First, I argue that early Heidegger makes use of three distinct concepts or spheres of history, namely (1) history as intergenerational process, (2) history as personal or autobiographical development, and (3) history as the real center and origin of all intentional acts in the intentional self. Second, I argue that an essential motif in Heidegger’s discussion is the re-appropriation of what he considers the externalized and expropriated historical reality in all three spheres. I suggest that this constitutes an objective parallelism to similar moves in Marx and neo-Marxist thought, especially Lukács and the Frankfurt School. I show that Heidegger is on his way towards an ethics of time. First, in opposition to theoretical historicism and historical aestheti-cism or determinism of his time, early Heidegger advocates the active historical participation in history, the engagement in one’s historical situation or praxis. Second, in opposition to the publically regimented and reified time frames, calendars and interpretations, Heidegger argues for the self-reflexive, historical shaping of one’s very own and unique life-time. Third, because Heidegger finds the origin of all history in the historical enactments of intentions in the intentional self, he ultimately argues for the self-reflexive acknowledgment of this ultimate historicity at the very heart of human intentionality, calling for the always renewed accentuation of this inevitable and ultimate historicity as a necessary condition for authentic temporality.En este artículo analizo el concepto de historia de Heidegger. Primero, argumento que el Heidegger temprano hace uso de tres conceptos distintos, o esferas, de historia, a saber, (1) la historia como proceso de interrogación, (2) la historia como desarrollo personal o autobiográfico y (3) la historia como el centro real y origen de todos los actos intencionales en el yo intencional. Segundo, argumento que un motivo esencial en la discusión de Heidegger es la re-apropiación de lo que considera la externalización y expropiación de la realidad histórica en las tres esferas. Sugiero que esto constituye un objetivo paralelo al de movimientos similares en Marx y el pensamiento neo-Marxista, especialmente Lukács y la Escuela de Frankfurt. Muestro que Heidegger está en este mismo camino hacia una ética del tiempo. Primero, en oposición al historicismo teórico y al esteticismo histórico o determinismo de su tiempo, el Heidegger temprano defiende la participación activa en la historia, el compromiso con la propia situación histórica o praxis. Segundo, en oposición a los marcos temporales, calendarios e interpretaciones regimentados y reificados, Heidegger defiende la auto-reflexión y la formación histórica del tiempo vital de uno mismo. Tercero, porque Heidegger encuentra el origen de toda historia en las realizaciones históricas de las intenciones del yo intencional, defiende en última instancia el reconocimiento auto-reflexivo de la historicidad en el núcleo íntimo de la intencionalidad humana, llamando a una siempre renovada acentuación de esta inevitable y última historicidad como una condición necesaria de la temporalidad auténtica.

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