Related Experiment Video
Updated: Jan 14, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
496
Composing α-Gauss and logistic maps: Gradual and sudden transitions to chaos
Marcelo A Pires1, Constantino Tsallis1,2,3,4, Evaldo M F Curado1,2
1Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil.
Physical Review. E
|October 21, 2025
Summary
We introduce the α-Gauss-Logistic map, a novel nonlinear dynamic system. Its behavior, depending on parameters r and α, ranges from period-doubling cascades to chaos and abrupt transitions, revealing rich phenomenology.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Mathematical Physics
Background:
- The logistic map and α-Gauss map are fundamental in nonlinear dynamics.
- Understanding complex system behavior through parameter variation is crucial.
Purpose of the Study:
- Introduce a novel nonlinear dynamics model, the α-Gauss-Logistic map.
- Investigate the system's phenomenology based on parameters r and α.
- Analyze the transition to chaos and properties of chaotic attractors.
Main Methods:
- Constructed the α-Gauss-Logistic map by composing logistic and α-Gauss maps.
- Analyzed system behavior across different ranges of the parameter α.
- Employed the Perron-Frobenius equation for analytical treatment when α=1.
Main Results:
- For α<1, observed period-doubling cascades to chaos with stability windows.
- For 1≤α<2, found abrupt onsets of chaos without bifurcations or stability windows.
- For α≥2, regular behavior is absent; α=1 allows analytical solutions for Lyapunov exponent and invariant density.
Conclusions:
- The α-Gauss-Logistic map exhibits diverse dynamical behaviors controlled by r and α.
- The golden ratio (Φ) is identified as a critical threshold for gap disappearance in chaotic regimes.
- Invariant density approaches a q-Gaussian (q=2, Cauchy distribution) at the edge of chaos in the abrupt transition regime.
Related Concept Videos
01:10Entropy Change in Reversible Processes
3.2K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.2K
01:16SFG Algebra
312
In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
312
02:39Entropy
34.9K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
34.9K
01:18Entropy
3.5K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.5K
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
284
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
284
01:13Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
287
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
287