scholarly journals Chaos in a simple model of a delta network

2020 ◽  
Vol 117 (44) ◽  
pp. 27179-27187
Author(s):  
Gerard Salter ◽  
Vaughan R. Voller ◽  
Chris Paola
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Fundamental Limits ◽  
Experimental Systems ◽  
Flux Partitioning ◽  
Sensitive Dependence ◽  
Statistical Behavior ◽  
The Mean ◽  
Simple Numerical Model

The flux partitioning in delta networks controls how deltas build land and generate stratigraphy. Here, we study flux-partitioning dynamics in a delta network using a simple numerical model consisting of two orders of bifurcations. Previous work on single bifurcations has shown periodic behavior arising due to the interplay between channel deepening and downstream deposition. We find that coupling between upstream and downstream bifurcations can lead to chaos; despite its simplicity, our model generates surprisingly complex aperiodic yet bounded dynamics. Our model exhibits sensitive dependence on initial conditions, the hallmark signature of chaos, implying long-term unpredictability of delta networks. However, estimates of the predictability horizon suggest substantial room for improvement in delta-network modeling before fundamental limits on predictability are encountered. We also observe periodic windows, implying that a change in forcing (e.g., due to climate change) could cause a delta to switch from predictable to unpredictable or vice versa. We test our model by using it to generate stratigraphy; converting the temporal Lyapunov exponent to vertical distance using the mean sedimentation rate, we observe qualitatively realistic patterns such as upwards fining and scale-dependent compensation statistics, consistent with ancient and experimental systems. We suggest that chaotic behavior may be common in geomorphic systems and that it implies fundamental bounds on their predictability. We conclude that while delta “weather” (precise configuration) is unpredictable in the long-term, delta “climate” (statistical behavior) is predictable.

scholarly journals Complexity In Psychological Self-Ratings: Implications for research and practice

2020 ◽  
Author(s):  
Merlijn Olthof ◽  
Fred Hasselman ◽  
Anna Lichtwarck-Aschoff
Keyword(s):  
Complex Systems ◽  
Systems Approach ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Regime Shifts ◽  
Fundamental Aspect ◽  
Time Varying ◽  
Term Prediction ◽  
Sensitive Dependence

Background: Psychopathology research is changing focus from group-based ‘disease models’ to a personalized approach inspired by complex systems theories. This approach, which has already produced novel and valuable insights into the complex nature of psychopathology, often relies on repeated self-ratings of individual patients. So far it has been unknown whether such self-ratings, the presumed observables of the individual patient as a complex system, actually display complex dynamics. We examine this basic assumption of a complex systems approach to psychopathology by testing repeated self-ratings for three markers of complexity: memory, the presence of (time-varying) short- and long-range temporal correlations, regime shifts, transitions between different dynamic regimes, and, sensitive dependence on initial conditions, also known as the ‘butterfly effect’, the divergence of initially similar trajectories.Methods: We analysed repeated self-ratings (1476 time points) from a single patient for the three markers of complexity using Bartels rank test, (partial) autocorrelation functions, time-varying autoregression, a non-stationarity test, change point analysis and the Sugihara-May algorithm.Results: Self-ratings concerning psychological states (e.g., the item ‘I feel down’) exhibited all complexity markers: time-varying short- and long-term memory, multiple regime shifts and sensitive dependence on initial conditions. Unexpectedly, self-ratings concerning physical sensations (e.g., the item ‘I am hungry’) exhibited less complex dynamics and their behaviour was more similar to random variables. Conclusions: Psychological self-ratings display complex dynamics. The presence of complexity in repeated self-ratings means that we have to acknowledge that (1) repeated self-ratings yield a complex pattern of data and not a set of (nearly) independent data points, (2) humans are ‘moving targets’ whose self-ratings display non-stationary change processes including regime shifts, and (3) long-term prediction of individual trajectories may be fundamentally impossible. These findings point to a limitation of popular statistical time series models whose assumptions are violated by the presence of these complexity markers. We conclude that a complex systems approach to mental health should appreciate complexity as a fundamental aspect of psychopathology research by adopting the models and methods of complexity science. Promising first steps in this direction, such as research on real-time process-monitoring, short-term prediction, and just-in-time interventions, are discussed.

CHAOTIC BEHAVIOR AND DYNAMICS OF MAPS USED IN A METHOD OF SCRAMBLING SIGNALS

2010 ◽  
Vol 20 (12) ◽  
pp. 4097-4101
Author(s):  
REZA MAZROOEI-SEBDANI ◽  
MEHDI DEHGHAN
Keyword(s):  
Fixed Points ◽  
Limit Cycles ◽  
Secure Communication ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Chaotic Encryption ◽  
Input And Output ◽  
Sensitive Dependence ◽  
Close Relationship ◽  
Existence And Stability

The close relationship between chaos and cryptography makes chaotic encryption a natural candidate for secure communication and cryptography. In this manuscript, we prove that a class of maps that have been proposed as suitable for scrambling signals possess the property of sensitive dependence on initial conditions (s.d.i.c.) necessary for chaos and cryptography. Our result can also be used for generating other maps with s.d.i.c., through a suitable semiconjugacy between their input and output parts. Using the condition of semiconjugacy we also establish for this class of maps rigorous criteria for the existence and stability of their fixed points and limit cycles.

Analyzing Devaney Chaos of a Sine–Cosine Compound Function System

2018 ◽  
Vol 28 (14) ◽  
pp. 1850176 ◽  
Author(s):  
Hegui Zhu ◽  
Wentao Qi ◽  
Jiangxia Ge ◽  
Yuelin Liu
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Function System ◽  
Topological Transitivity ◽  
One Dimensional ◽  
Devaney’S Chaos ◽  
Chebyshev Map ◽  
Sensitive Dependence ◽  
Sine Map ◽  
The One

The one-dimensional Sine map and Chebyshev map are classical chaotic maps, which have clear chaotic characteristics. In this paper, we establish a chaotic framework based on a Sine–Cosine compound function system by analyzing the existing one-dimensional Sine map and Chebyshev map. The sensitive dependence on initial conditions, topological transitivity and periodic-point density of this chaotic framework is proved, showing that the chaotic framework satisfies Devaney’s chaos definition. In order to illustrate the chaotic behavior of the chaotic framework, we propose three examples, called Cosine–Polynomial (C–P) map, Sine–Tangent (S–T) map and Sine–Exponent (S–E) map, respectively. Then, we evaluate the chaotic behavior with Sine map and Chebyshev map by analyzing bifurcation diagrams, Lyapunov exponents, correlation dimensions, Kolmogorov entropy and [Formula: see text] complexity. Experimental results show that the chaotic framework has better unpredictability and more complex chaotic behaviors than the classical Sine map and Chebyshev map. The results also verify the effectiveness of the theoretical analysis of the proposed chaotic framework.

What Could Be Worse than the Butterfly Effect?

2008 ◽  
Vol 38 (4) ◽  
pp. 519-547 ◽  
Author(s):  
Robert C. Bishop
Keyword(s):  
Nonlinear Systems ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Classical Mechanics ◽  
Physical Systems ◽  
Physics Community ◽  
Sensitive Dependence ◽  
Classical Models ◽  
In The Beginning

Our understanding of classical mechanics (CM) has undergone significant growth in the latter half of the twentieth century and in the beginning of the twenty-first. This growth has much to do with the explosion of interest in the study of nonlinear systems in contrast with the focus on linear systems that had colored much work in CM from its inception. For example, although Maxwell and Poincaré arguably were some of the first to think about chaotic behavior, the modern study of chaotic dynamics traces its beginning to the pioneering work of Edward Lorenz (1963). This work has yielded a rich variety of behavior in relatively simple classical models that was previously unsuspected by the vast majority of the physics community (see Hilborn 2001). Chaos is a property of nonlinear systems that is usually characterized by sensitive dependence on initial conditions (SDIC). In CM the behavior of simple physical systems is described using models (such as the harmonic oscillator) that capture the main features of the systems in question (Giere 1988).

Global Predictability of Chaotic Epidemiological Dynamics in Coupled Populations

2003 ◽  
Vol 10 (04) ◽  
pp. 311-320
Author(s):  
Matt Davison ◽  
C. Essex ◽  
J. S. Shiner
Keyword(s):  
Standard Deviation ◽  
Probability Distribution ◽  
Coupling Strength ◽  
Chaotic Dynamics ◽  
Statistical Measures ◽  
Sensitive Dependence ◽  
Strength Dependence ◽  
The Mean ◽  
Long Term Prediction

When the dynamics of an epidemic are chaotic, detailed prediction is effectively impossible, except perhaps in the short term. However, a probability distribution underlying the motion does allow for the long term prediction of statistical measures such as the mean or the standard deviation. Even this weaker long term predictability might be lost if distinct populations with chaotic dynamics are coupled. We show that such coupling can result in a phenomenon we call “sensitive dependence on neglected dynamics”. In light of this phenomenon, it is somewhat surprising that when two logistic maps are coupled, the long term predictability of the mean and standard deviation is maintained. This is true even though the probability distribution describing the time series depends on the coupling strength. The coupling-strength dependence does reveal itself in the loss of predictability of higher order moments such as skewness and kurtosis.

Effects of Discount Scenarios on Chaotic Behavior of Inventory Level Under Price-Dependent Demand

2013 ◽  
Vol 2 (3) ◽  
pp. 58-72
Author(s):  
Iman Nosoohi ◽  
Jamshid Parvizian
Keyword(s):  
Dynamic Model ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Inventory Level ◽  
Dependent Demand

In competitive conditions, demand depends on the price and retailers with lower prices sell more. In this paper a dynamic model is developed in which demand is price-dependent and the price is determined by the retailer based on its inventory level. The retailer can offer discounts to customers, regarding its inventory level, based on different scenarios such as linear, total or increasing scenarios. Simulations show that each scenario has different effects on the long-term chaotic behavior of the inventory level, and is able to control aperiodic behavior of inventory level under specific initial conditions. It is established that in order to secure inventory stability, the discount scenario should consider the incoming shipments to the retailer and the potentially maximum demand, instead of the inventory level.

scholarly journals Complexity in psychological self-ratings: implications for research and practice

BMC Medicine ◽  
2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Merlijn Olthof ◽  
Fred Hasselman ◽  
Anna Lichtwarck-Aschoff
Keyword(s):  
Complex Systems ◽  
Systems Approach ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Regime Shifts ◽  
Fundamental Aspect ◽  
Time Varying ◽  
Term Prediction ◽  
Sensitive Dependence

Abstract Background Psychopathology research is changing focus from group-based “disease models” to a personalized approach inspired by complex systems theories. This approach, which has already produced novel and valuable insights into the complex nature of psychopathology, often relies on repeated self-ratings of individual patients. So far, it has been unknown whether such self-ratings, the presumed observables of the individual patient as a complex system, actually display complex dynamics. We examine this basic assumption of a complex systems approach to psychopathology by testing repeated self-ratings for three markers of complexity: memory, the presence of (time-varying) short- and long-range temporal correlations; regime shifts, transitions between different dynamic regimes; and sensitive dependence on initial conditions, also known as the “butterfly effect,” the divergence of initially similar trajectories. Methods We analyzed repeated self-ratings (1476 time points) from a single patient for the three markers of complexity using Bartels rank test, (partial) autocorrelation functions, time-varying autoregression, a non-stationarity test, change point analysis, and the Sugihara-May algorithm. Results Self-ratings concerning psychological states (e.g., the item “I feel down”) exhibited all complexity markers: time-varying short- and long-term memory, multiple regime shifts, and sensitive dependence on initial conditions. Unexpectedly, self-ratings concerning physical sensations (e.g., the item “I am hungry”) exhibited less complex dynamics and their behavior was more similar to random variables. Conclusions Psychological self-ratings display complex dynamics. The presence of complexity in repeated self-ratings means that we have to acknowledge that (1) repeated self-ratings yield a complex pattern of data and not a set of (nearly) independent data points, (2) humans are “moving targets” whose self-ratings display non-stationary change processes including regime shifts, and (3) long-term prediction of individual trajectories may be fundamentally impossible. These findings point to a limitation of popular statistical time series models whose assumptions are violated by the presence of these complexity markers. We conclude that a complex systems approach to mental health should appreciate complexity as a fundamental aspect of psychopathology research by adopting the models and methods of complexity science. Promising first steps in this direction, such as research on real-time process monitoring, short-term prediction, and just-in-time interventions, are discussed.

scholarly journals On Relation between No-Arbitrage Pricing Principle and Modigliani-Miller Propositions

2020 ◽  
Vol 9 (1) ◽  
pp. 148-174
Author(s):  
Valery Shemetov
Keyword(s):  
Firm Value ◽  
Initial Conditions ◽  
Business Environment ◽  
Time Intervals ◽  
No Arbitrage ◽  
Bankruptcy Costs ◽  
Brownian Model ◽  
The Mean ◽  
Short Time

An extension of Merton’s (1974) model (EMM) taking account of the firm’s payments and generating a new statistical distribution for the firm value is suggested. In an open log-value space, this distribution evolves from the initially normal to negatively skewed one. When payments are zero or proportional to the firm value, EMM turns into the Geometric Brownian model (GBM). We show that Modigliani-Miller Propositions (MMPs) and the no-arbitraging principle (NAP) result from the use of GBM with no payments. For a firm with payments, MMPs hold for short times and are false for time intervals exceeding a year. In contradiction with MMPs, the asset structure affects the firm value at the perfect market, and at the market with taxes, debt decreases the firm value even when there are no bankruptcy costs. NAP always holds for the entire market for short time deals. For long-term investments, the firm’s mean year returns decline in time intervals whose length depends on the firm’s initial conditions and its business environment. In these conditions, NAP does not hold for the whole market, but it temporarily holds for individual stocks as far as the mean year returns of the firms issuing them remain constant and fails when the mean year returns begin to decline.

On Invariant Qualitative Chaos in Multi-Black-Hole Spacetimes

1997 ◽  
Vol 06 (06) ◽  
pp. 741-770 ◽  
Author(s):  
Marek Szydłowski
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Optical Model ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Cylindrical Symmetry ◽  
Geodesic Motion ◽  
Local Instability ◽  
Black Hole Spacetimes ◽  
Sensitive Dependence

It is analytically shown when chaos exists in the behavior of null and timelike geodesics in the general case of geodesic motion in static and diagonal fields of general relativity. We demonstrate the effectiveness of our method of investigating chaos in the behavior of geodesic motion in the multi-black-hole spacetimes. An optical model of chaotic behavior of geodesics in spacetimes with cylindrical symmetry is presented. The Lyapunov characteristic time is defined and estimated for geodesic motion of a test particle in the external fields of general relativity. We find that its value is positive in some compact regions of the configuration space. This means that the trajectories have the property of local instability which implies the sensitive dependence on initial conditions.

Acute and Chronic Changes in Platelet Volume and Count After Cardiopulmonary Bypass Induced Thrombocytopenia in Man

1987 ◽  
Vol 57 (01) ◽  
pp. 55-58 ◽  
Author(s):  
J F Martin ◽  
T D Daniel ◽  
E A Trowbridge
Keyword(s):  
Platelet Count ◽  
Mean Platelet Volume ◽  
Artery Bypass ◽  
Bypass Graft ◽  
Control Group ◽  
Artery Bypass Graft ◽  
Platelet Volume ◽  
Young Males ◽  
The Mean

SummaryPatients undergoing surgery for coronary artery bypass graft or heart valve replacement had their platelet count and mean volume measured pre-operatively, immediately post-operatively and serially for up to 48 days after the surgical procedure. The mean pre-operative platelet count of 1.95 ± 0.11 × 1011/1 (n = 26) fell significantly to 1.35 ± 0.09 × 1011/1 immediately post-operatively (p <0.001) (n = 22), without a significant alteration in the mean platelet volume. The average platelet count rose to a maximum of 5.07 ± 0.66 × 1011/1 between days 14 and 17 after surgery while the average mean platelet volume fell from preparative and post-operative values of 7.25 ± 0.14 and 7.20 ± 0.14 fl respectively to a minimum of 6.16 ± 0.16 fl by day 20. Seven patients were followed for 32 days or longer after the operation. By this time they had achieved steady state thrombopoiesis and their average platelet count was 2.44 ± 0.33 × 1011/1, significantly higher than the pre-operative value (p <0.05), while their average mean platelet volume was 6.63 ± 0.21 fl, significantly lower than before surgery (p <0.001). The pre-operative values for the platelet volume and counts of these patients were significantly different from a control group of 32 young males, while the chronic post-operative values were not. These long term changes in platelet volume and count may reflect changes in the thrombopoietic control system secondary to the corrective surgery.

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