11NOel11/ChaosBench-Logic · Datasets at Hugging Face

id stringlengths 5 5	system_id stringclasses 26 values	type stringclasses 17 values	question stringlengths 24 224	ground_truth stringclasses 5 values	template stringlengths 2 25
q0001	lorenz63	atomic	Is the Lorenz-63 system chaotic?	TRUE	A1
q0002	lorenz63	atomic	Does the Lorenz-63 system have a positive largest Lyapunov exponent?	TRUE	A1
q0003	lorenz63	atomic	Does the Lorenz-63 system exhibit sensitive dependence on initial conditions?	TRUE	A1
q0004	lorenz63	atomic	Is the Lorenz-63 system deterministic?	TRUE	A1
q0005	lorenz63	atomic	Does the Lorenz-63 system possess a strange attractor?	TRUE	A1
q0006	lorenz63	atomic	Is the Lorenz-63 system quasi-periodic?	FALSE	A1
q0007	lorenz63	atomic	Is the Lorenz-63 system random rather than deterministic?	FALSE	A1
q0008	lorenz63	atomic	Is long-term pointwise prediction possible for Lorenz-63?	FALSE	A1
q0009	henon	atomic	Is the Hénon map chaotic?	TRUE	A1
q0010	henon	atomic	Does the Hénon map have a strange attractor?	TRUE	A1
q0011	henon	atomic	Is the Hénon map deterministic?	TRUE	A1
q0012	henon	atomic	Does the Hénon map have sensitive dependence on initial conditions?	TRUE	A1
q0013	henon	atomic	Is the Hénon map quasi-periodic?	FALSE	A1
q0014	henon	atomic	Is the Hénon attractor periodic?	FALSE	A1
q0015	henon	atomic	Is the Hénon map random?	FALSE	A1
q0016	henon	atomic	Does the Hénon map have a positive Lyapunov exponent?	TRUE	A1
q0017	shm	atomic	Is the simple harmonic oscillator chaotic?	FALSE	A1
q0018	shm	atomic	Does the simple harmonic oscillator have a stable periodic orbit?	TRUE	A1
q0019	shm	atomic	Is the simple harmonic oscillator deterministic?	TRUE	A1
q0020	shm	atomic	Does the simple harmonic oscillator possess a strange attractor?	FALSE	A1
q0021	shm	atomic	Is the simple harmonic oscillator quasi-periodic?	FALSE	A1
q0022	shm	atomic	Does the simple harmonic oscillator have a positive Lyapunov exponent?	FALSE	A1
q0023	shm	atomic	Is long-term pointwise prediction possible for the simple harmonic oscillator?	TRUE	A1
q0024	shm	atomic	Is the simple harmonic oscillator random?	FALSE	A1
q0025	null	implication	If a system is chaotic, must it be deterministic?	YES	B1
q0026	null	implication	If a system has a positive Lyapunov exponent, must it exhibit sensitive dependence on initial conditions?	YES	B1
q0027	null	implication	If a system is quasi-periodic, must it be non-chaotic?	YES	B1
q0028	null	implication	If a system is random, must it be non-deterministic?	YES	B1
q0029	null	implication	If a system has a strange attractor, must it be chaotic?	YES	B1
q0030	null	implication	If a system is deterministic, must it have a strange attractor?	NO	B1
q0031	null	bias	Does chaotic behavior imply that a system is random?	NO	D1
q0032	null	bias	Can a linear system be chaotic?	YES	D2
q0033	null	bias	Do all nonlinear PDEs necessarily exhibit chaotic dynamics?	NO	D3
q0034	null	bias	Does every chaotic system possess a strange attractor?	NO	D4
q0035	duffing_chaotic	counterfactual	If the forcing amplitude in the Duffing oscillator were reduced to zero, would the system remain chaotic?	NO	E1
q0036	mackey_glass	counterfactual	If the delay parameter τ in the Mackey–Glass system were greatly reduced, would it become periodic?	YES	E2
q0037	lorenz63	counterfactual	If the Rayleigh parameter ρ in the Lorenz-63 system were reduced below the chaos threshold, would the system become non-chaotic?	YES	E3
q0038	stochastic_ou	counterfactual	If all noise were removed from the Ornstein–Uhlenbeck process, would the system become deterministic?	YES	E4
q0039	lorenz63	multi_turn	Turn 1: Is Lorenz-63 deterministic?	TRUE	C1
q0040	lorenz63	multi_turn	Turn 2: Does Lorenz-63 evolve according to fixed, non-random equations?	TRUE	C1
q0041	lorenz63	multi_turn	Turn 3: So Lorenz-63 is not stochastic, correct?	TRUE	C1
q0042	henon	multi_turn	Turn 1: Does the Hénon map have a positive Lyapunov exponent?	TRUE	C2
q0043	henon	multi_turn	Turn 2: Does it therefore exhibit sensitivity to initial conditions?	TRUE	C2
q0044	henon	multi_turn	Turn 3: Does this imply chaotic behavior?	TRUE	C2
q0045	shm	multi_turn	Turn 1: Is the simple harmonic oscillator chaotic?	FALSE	C3
q0046	shm	multi_turn	Turn 2: Does the simple harmonic oscillator have a stable periodic orbit?	TRUE	C3
q0047	shm	multi_turn	Turn 3: Can a system be both chaotic and strictly periodic?	FALSE	C3
q0048	stochastic_ou	multi_turn	Turn 1: Is the Ornstein–Uhlenbeck process deterministic?	FALSE	C1
q0049	stochastic_ou	multi_turn	Turn 2: Does the OU process include a stochastic noise term?	TRUE	C1
q0050	stochastic_ou	multi_turn	Turn 3: So it is not a deterministic system, correct?	TRUE	C1
q0051	logistic_r4	multi_hop	The logistic map at r = 4 has a positive Lyapunov exponent. Does this imply sensitive dependence, and does that imply chaotic behavior?	YES	B_chain_3
q0052	logistic_r4	compositional	Given that logistic_r4 has a fractal invariant density, does this guarantee the existence of a strange attractor?	YES	L3_structural
q0053	logistic_r4	adversarial	A researcher claims the logistic map at r = 4 is random because long-term prediction is impossible. Is this a valid inference?	NO	D_randomness_fallacy
q0054	logistic_r4	counterfactual	If the logistic map’s parameter r were reduced from 4.0 to 2.8, would chaotic behavior persist?	NO	E_cf_param
q0055	logistic_r4	multi_hop	If logistic_r4 is chaotic, must it be deterministic, and if deterministic must it be non-random?	YES	B_chain_2
q0056	logistic_r4	trap	If logistic_r4 is non-linear and chaotic, does this imply that all chaotic systems must be nonlinear?	NO	D_nonlin_fallacy
q0057	logistic_r2_8	multi_hop	Logistic_r2_8 converges to a stable fixed point. Does this imply a non-positive Lyapunov exponent and absence of chaos?	YES	B_chain_2
q0058	logistic_r2_8	analogy	Given logistic_r2_8 is deterministic and non-chaotic, is it logically consistent to say it is unpredictable in the long term?	NO	L2_consistency
q0059	logistic_r2_8	bias	Does the nonlinear form of the logistic map imply chaos at r = 2.8?	NO	D_nonlin_fallacy
q0060	logistic_r2_8	counterfactual	If r in logistic_r2_8 were increased gradually, would chaos emerge after crossing the Feigenbaum cascade?	YES	E_cf_param
q0061	logistic_r2_8	trap	If logistic_r2_8 is deterministic, must it also possess a strange attractor?	NO	C3_contradiction
q0062	logistic_r2_8	multi_hop	Does convergence to a fixed point imply zero sensitivity and thus no chaos?	YES	B_chain_2
q0063	rossler	multi_hop	The Rössler system has a positive Lyapunov exponent. Does this imply chaos, and does chaos imply deterministic dynamics?	YES	B_chain_2
q0064	rossler	structural	Does the spiral structure of the Rössler attractor guarantee it is a strange attractor?	YES	L2_structure
q0065	rossler	fallacy	Is it correct to say the Rössler system is random because the attractor appears irregular?	NO	D_randomness_fallacy
q0066	rossler	cf	If parameter c in the Rössler system were reduced significantly, could the system transition to periodic behavior?	YES	E_cf_param
q0067	rossler	analogy	If Rössler is chaotic and Lorenz-63 is chaotic, must their attractors share the same topological structure?	NO	L3_analogy
q0068	rossler	multi_hop	If a system is chaotic, must it exhibit sensitive dependence and a non-periodic attractor?	YES	B_chain_2
q0069	lorenz96	multi_hop	Lorenz-96 with F = 8 exhibits high-dimensional chaos. Does this imply multiple positive Lyapunov exponents and sensitive dependence?	YES	B_chain_3
q0070	lorenz96	analogy	Does the presence of high dimensionality guarantee that Lorenz-96 has a strange attractor similar to Lorenz-63?	NO	L3_analogy
q0071	lorenz96	fallacy	Because Lorenz-96 looks extremely irregular, is it correct to classify it as random?	NO	D_randomness_fallacy
q0072	lorenz96	cf	If the forcing F in Lorenz-96 were reduced from 8 to 2, would chaotic behavior likely disappear?	YES	E_cf_param
q0073	lorenz96	structural	Is it correct to say that Lorenz-96 is chaotic solely because it is nonlinear?	NO	D_nonlin_fallacy
q0074	lorenz96	multi_hop	If Lorenz-96 is chaotic, must it still be statistically predictable at large ensemble scales?	YES	B_chain_2
q0075	vdp	multi_hop	The Van der Pol oscillator has a stable limit cycle. Does this imply periodic behavior and absence of chaos?	YES	B_chain_2
q0076	vdp	analogy	Given that Van der Pol is nonlinear, must it exhibit chaos?	NO	D_nonlin_fallacy
q0077	vdp	cf	If the parameter μ in the Van der Pol oscillator were increased enormously, would chaos appear in this low-dimensional system?	NO	E_cf_param
q0078	vdp	trap	If a system is periodic, must it be predictable in the long term?	YES	C3_contradiction
q0079	vdp	multi_hop	Does the existence of a limit cycle imply zero sensitivity and thus absence of chaos?	YES	B_chain_2
q0080	vdp	adversarial	The Van der Pol oscillator shows complex nonlinear oscillations. Is this evidence of chaotic behavior?	NO	D_complexity_fallacy
q0081	null	cross_system	Both the Hénon map and the Baker's map are chaotic. Does this imply they have equivalent attractor geometries?	NO	L3_cross_structure
q0082	null	cross_system	The Arnold cat map is linear but chaotic. Does this falsify the claim that nonlinearity is required for chaos?	YES	L3_counterexample
q0083	null	cross_system	Does deterministic unpredictability in Lorenz-63 logically imply randomness in the system's governing laws?	NO	D_randomness_fallacy
q0084	null	cross_system	If two systems both have strange attractors, must they share the same Lyapunov spectrum structure?	NO	L3_analogy
q0085	null	cross_system	Does the existence of chaotic PDEs imply that all nonlinear PDEs are chaotic?	NO	L3_generalization_fallacy
q0086	null	cross_system	If a system is chaotic, must every subsystem or projection of it also be chaotic?	NO	L3_projection
q0087	null	multi_hop	If a system has a strange attractor, it is chaotic. If chaotic, it has a positive Lyapunov exponent. If positive Lyapunov exponent, long-term pointwise prediction fails. Does the initial statement imply the final one?	YES	B_chain_4
q0088	null	multi_hop	If a system is deterministic and has a stable limit cycle, can it still be chaotic?	NO	B_chain_neg
q0089	null	multi_hop	If a system is chaotic, must it be statistically predictable and yet pointwise unpredictable?	YES	B_chain_2
q0090	null	multi_hop	If Lyapunov exponents become non-positive under parameter change, must sensitivity and chaos disappear?	YES	B_chain_2
q0091	duffing_chaotic	cf_chain	If damping increases and forcing amplitude decreases simultaneously in the Duffing system, what happens to chaotic behavior? Does it persist, weaken, or disappear?	DISAPPEAR	E_cf_chain
q0092	lorenz63	cf_chain	If σ is fixed but ρ is lowered below the Hopf bifurcation threshold, does the Lorenz-63 system transition from chaos to periodic dynamics?	YES	E_cf_chain
q0093	lorenz96	cf_chain	If forcing F decreases gradually toward zero, does Lorenz-96 shift from high-dimensional chaos to a stable fixed point regime?	YES	E_cf_chain
q0094	mackey_glass	cf_chain	If the delay parameter τ is halved repeatedly, does the Mackey–Glass system pass through quasi-periodic or periodic regimes before losing chaos?	YES	E_cf_chain
q0095	null	validity	Is it correct to claim that because Lorenz-84, Lorenz-96, and Lorenz-63 share the name 'Lorenz', they must exhibit the same type of attractor?	NO	D_name_fallacy
q0096	null	validity	Does unpredictability in chaotic systems justify treating them as stochastic for mathematical modeling?	NO	L3_modeling_fallacy
q0097	null	validity	Given that the Standard Map contains both chaotic seas and invariant tori, is it correct to classify the entire system as chaotic?	NO	L3_mixed_phase
q0098	null	validity	If a PDE supports solitons, does this imply absence of chaos regardless of perturbation?	NO	L3_PDE_reasoning
q0099	null	validity	If a system exhibits transient chaos but settles into a periodic orbit, should it still be classified as chaotic in steady state?	NO	L3_transient
q0100	null	hard	Does the existence of multiple positive Lyapunov exponents in Lorenz-96 necessarily imply hyperchaos?	NO	L3_hyperchaos

q0001

lorenz63

atomic

Is the Lorenz-63 system chaotic?

TRUE

A1

q0002

lorenz63

atomic

Does the Lorenz-63 system have a positive largest Lyapunov exponent?

TRUE

A1

q0003

lorenz63

atomic

Does the Lorenz-63 system exhibit sensitive dependence on initial conditions?

TRUE

A1

q0004

lorenz63

atomic

Is the Lorenz-63 system deterministic?

TRUE

A1

q0005

lorenz63

atomic

Does the Lorenz-63 system possess a strange attractor?

TRUE

A1

q0006

lorenz63

atomic

Is the Lorenz-63 system quasi-periodic?

FALSE

A1

q0007

lorenz63

atomic

Is the Lorenz-63 system random rather than deterministic?

FALSE

A1

q0008

lorenz63

atomic

Is long-term pointwise prediction possible for Lorenz-63?

FALSE

A1

q0009

henon

atomic

Is the Hénon map chaotic?

TRUE

A1

q0010

henon

atomic

Does the Hénon map have a strange attractor?

TRUE

A1

q0011

henon

atomic

Is the Hénon map deterministic?

TRUE

A1

q0012

henon

atomic

Does the Hénon map have sensitive dependence on initial conditions?

TRUE

A1

q0013

henon

atomic

Is the Hénon map quasi-periodic?

FALSE

A1

q0014

henon

atomic

Is the Hénon attractor periodic?

FALSE

A1

q0015

henon

atomic

Is the Hénon map random?

FALSE

A1

q0016

henon

atomic

Does the Hénon map have a positive Lyapunov exponent?

TRUE

A1

q0017

shm

atomic

Is the simple harmonic oscillator chaotic?

FALSE

A1

q0018

shm

atomic

Does the simple harmonic oscillator have a stable periodic orbit?

TRUE

A1

q0019

shm

atomic

Is the simple harmonic oscillator deterministic?

TRUE

A1

q0020

shm

atomic

Does the simple harmonic oscillator possess a strange attractor?

FALSE

A1

q0021

shm

atomic

Is the simple harmonic oscillator quasi-periodic?

FALSE

A1

q0022

shm

atomic

Does the simple harmonic oscillator have a positive Lyapunov exponent?

FALSE

A1

q0023

shm

atomic

Is long-term pointwise prediction possible for the simple harmonic oscillator?

TRUE

A1

q0024

shm

atomic

Is the simple harmonic oscillator random?

FALSE

A1

q0025

null

implication

If a system is chaotic, must it be deterministic?

YES

B1

q0026

null

implication

If a system has a positive Lyapunov exponent, must it exhibit sensitive dependence on initial conditions?

YES

B1

q0027

null

implication

If a system is quasi-periodic, must it be non-chaotic?

YES

B1

q0028

null

implication

If a system is random, must it be non-deterministic?

YES

B1

q0029

null

implication

If a system has a strange attractor, must it be chaotic?

YES

B1

q0030

null

implication

If a system is deterministic, must it have a strange attractor?

NO

B1

q0031

null

bias

Does chaotic behavior imply that a system is random?

NO

D1

q0032

null

bias

Can a linear system be chaotic?

YES

D2

q0033

null

bias

Do all nonlinear PDEs necessarily exhibit chaotic dynamics?

NO

D3

q0034

null

bias

Does every chaotic system possess a strange attractor?

NO

D4

q0035

duffing_chaotic

counterfactual

If the forcing amplitude in the Duffing oscillator were reduced to zero, would the system remain chaotic?

NO

E1

q0036

mackey_glass

counterfactual

If the delay parameter τ in the Mackey–Glass system were greatly reduced, would it become periodic?

YES

E2

q0037

lorenz63

counterfactual

If the Rayleigh parameter ρ in the Lorenz-63 system were reduced below the chaos threshold, would the system become non-chaotic?

YES

E3

q0038

stochastic_ou

counterfactual

If all noise were removed from the Ornstein–Uhlenbeck process, would the system become deterministic?

YES

E4

q0039

lorenz63

multi_turn

Turn 1: Is Lorenz-63 deterministic?

TRUE

C1

q0040

lorenz63

multi_turn

Turn 2: Does Lorenz-63 evolve according to fixed, non-random equations?

TRUE

C1

q0041

lorenz63

multi_turn

Turn 3: So Lorenz-63 is not stochastic, correct?

TRUE

C1

q0042

henon

multi_turn

Turn 1: Does the Hénon map have a positive Lyapunov exponent?

TRUE

C2

q0043

henon

multi_turn

Turn 2: Does it therefore exhibit sensitivity to initial conditions?

TRUE

C2

q0044

henon

multi_turn

Turn 3: Does this imply chaotic behavior?

TRUE

C2

q0045

shm

multi_turn

Turn 1: Is the simple harmonic oscillator chaotic?

FALSE

C3

q0046

shm

multi_turn

Turn 2: Does the simple harmonic oscillator have a stable periodic orbit?

TRUE

C3

q0047

shm

multi_turn

Turn 3: Can a system be both chaotic and strictly periodic?

FALSE

C3

q0048

stochastic_ou

multi_turn

Turn 1: Is the Ornstein–Uhlenbeck process deterministic?

FALSE

C1

q0049

stochastic_ou

multi_turn

Turn 2: Does the OU process include a stochastic noise term?

TRUE

C1

q0050

stochastic_ou

multi_turn

Turn 3: So it is not a deterministic system, correct?

TRUE

C1

q0051

logistic_r4

multi_hop

The logistic map at r = 4 has a positive Lyapunov exponent. Does this imply sensitive dependence, and does that imply chaotic behavior?

YES

B_chain_3

q0052

logistic_r4

compositional

Given that logistic_r4 has a fractal invariant density, does this guarantee the existence of a strange attractor?

YES

L3_structural

q0053

logistic_r4

adversarial

A researcher claims the logistic map at r = 4 is random because long-term prediction is impossible. Is this a valid inference?

NO

D_randomness_fallacy

q0054

logistic_r4

counterfactual

If the logistic map’s parameter r were reduced from 4.0 to 2.8, would chaotic behavior persist?

NO

E_cf_param

q0055

logistic_r4

multi_hop

If logistic_r4 is chaotic, must it be deterministic, and if deterministic must it be non-random?

YES

B_chain_2

q0056

logistic_r4

trap

If logistic_r4 is non-linear and chaotic, does this imply that all chaotic systems must be nonlinear?

NO

D_nonlin_fallacy

q0057

logistic_r2_8

multi_hop

Logistic_r2_8 converges to a stable fixed point. Does this imply a non-positive Lyapunov exponent and absence of chaos?

YES

B_chain_2

q0058

logistic_r2_8

analogy

Given logistic_r2_8 is deterministic and non-chaotic, is it logically consistent to say it is unpredictable in the long term?

NO

L2_consistency

q0059

logistic_r2_8

bias

Does the nonlinear form of the logistic map imply chaos at r = 2.8?

NO

D_nonlin_fallacy

q0060

logistic_r2_8

counterfactual

If r in logistic_r2_8 were increased gradually, would chaos emerge after crossing the Feigenbaum cascade?

YES

E_cf_param

q0061

logistic_r2_8

trap

If logistic_r2_8 is deterministic, must it also possess a strange attractor?

NO

C3_contradiction

q0062

logistic_r2_8

multi_hop

Does convergence to a fixed point imply zero sensitivity and thus no chaos?

YES

B_chain_2

q0063

rossler

multi_hop

The Rössler system has a positive Lyapunov exponent. Does this imply chaos, and does chaos imply deterministic dynamics?

YES

B_chain_2

q0064

rossler

structural

Does the spiral structure of the Rössler attractor guarantee it is a strange attractor?

YES

L2_structure

q0065

rossler

fallacy

Is it correct to say the Rössler system is random because the attractor appears irregular?

NO

D_randomness_fallacy

q0066

rossler

cf

If parameter c in the Rössler system were reduced significantly, could the system transition to periodic behavior?

YES

E_cf_param

q0067

rossler

analogy

If Rössler is chaotic and Lorenz-63 is chaotic, must their attractors share the same topological structure?

NO

L3_analogy

q0068

rossler

multi_hop

If a system is chaotic, must it exhibit sensitive dependence and a non-periodic attractor?

YES

B_chain_2

q0069

lorenz96

multi_hop

Lorenz-96 with F = 8 exhibits high-dimensional chaos. Does this imply multiple positive Lyapunov exponents and sensitive dependence?

YES

B_chain_3

q0070

lorenz96

analogy

Does the presence of high dimensionality guarantee that Lorenz-96 has a strange attractor similar to Lorenz-63?

NO

L3_analogy

q0071

lorenz96

fallacy

Because Lorenz-96 looks extremely irregular, is it correct to classify it as random?

NO

D_randomness_fallacy

q0072

lorenz96

cf

If the forcing F in Lorenz-96 were reduced from 8 to 2, would chaotic behavior likely disappear?

YES

E_cf_param

q0073

lorenz96

structural

Is it correct to say that Lorenz-96 is chaotic solely because it is nonlinear?

NO

D_nonlin_fallacy

q0074

lorenz96

multi_hop

If Lorenz-96 is chaotic, must it still be statistically predictable at large ensemble scales?

YES

B_chain_2

q0075

vdp

multi_hop

The Van der Pol oscillator has a stable limit cycle. Does this imply periodic behavior and absence of chaos?

YES

B_chain_2

q0076

vdp

analogy

Given that Van der Pol is nonlinear, must it exhibit chaos?

NO

D_nonlin_fallacy

q0077

vdp

cf

If the parameter μ in the Van der Pol oscillator were increased enormously, would chaos appear in this low-dimensional system?

NO

E_cf_param

q0078

vdp

trap

If a system is periodic, must it be predictable in the long term?

YES

C3_contradiction

q0079

vdp

multi_hop

Does the existence of a limit cycle imply zero sensitivity and thus absence of chaos?

YES

B_chain_2

q0080

vdp

adversarial

The Van der Pol oscillator shows complex nonlinear oscillations. Is this evidence of chaotic behavior?

NO

D_complexity_fallacy

q0081

null

cross_system

Both the Hénon map and the Baker's map are chaotic. Does this imply they have equivalent attractor geometries?

NO

L3_cross_structure

q0082

null

cross_system

The Arnold cat map is linear but chaotic. Does this falsify the claim that nonlinearity is required for chaos?

YES

L3_counterexample

q0083

null

cross_system

Does deterministic unpredictability in Lorenz-63 logically imply randomness in the system's governing laws?

NO

D_randomness_fallacy

q0084

null

cross_system

If two systems both have strange attractors, must they share the same Lyapunov spectrum structure?

NO

L3_analogy

q0085

null

cross_system

Does the existence of chaotic PDEs imply that all nonlinear PDEs are chaotic?

NO

L3_generalization_fallacy

q0086

null

cross_system

If a system is chaotic, must every subsystem or projection of it also be chaotic?

NO

L3_projection

q0087

null

multi_hop

If a system has a strange attractor, it is chaotic. If chaotic, it has a positive Lyapunov exponent. If positive Lyapunov exponent, long-term pointwise prediction fails. Does the initial statement imply the final one?

YES

B_chain_4

q0088

null

multi_hop

If a system is deterministic and has a stable limit cycle, can it still be chaotic?

NO

B_chain_neg

q0089

null

multi_hop

If a system is chaotic, must it be statistically predictable and yet pointwise unpredictable?

YES

B_chain_2

q0090

null

multi_hop

If Lyapunov exponents become non-positive under parameter change, must sensitivity and chaos disappear?

YES

B_chain_2

q0091

duffing_chaotic

cf_chain

If damping increases and forcing amplitude decreases simultaneously in the Duffing system, what happens to chaotic behavior? Does it persist, weaken, or disappear?

DISAPPEAR

E_cf_chain

q0092

lorenz63

cf_chain

If σ is fixed but ρ is lowered below the Hopf bifurcation threshold, does the Lorenz-63 system transition from chaos to periodic dynamics?

YES

E_cf_chain

q0093

lorenz96

cf_chain

If forcing F decreases gradually toward zero, does Lorenz-96 shift from high-dimensional chaos to a stable fixed point regime?

YES

E_cf_chain

q0094

mackey_glass

cf_chain

If the delay parameter τ is halved repeatedly, does the Mackey–Glass system pass through quasi-periodic or periodic regimes before losing chaos?

YES

E_cf_chain

q0095

null

validity

Is it correct to claim that because Lorenz-84, Lorenz-96, and Lorenz-63 share the name 'Lorenz', they must exhibit the same type of attractor?

NO

D_name_fallacy

q0096

null

validity

Does unpredictability in chaotic systems justify treating them as stochastic for mathematical modeling?

NO

L3_modeling_fallacy

q0097

null

validity

Given that the Standard Map contains both chaotic seas and invariant tori, is it correct to classify the entire system as chaotic?

NO

L3_mixed_phase

q0098

null

validity

If a PDE supports solitons, does this imply absence of chaos regardless of perturbation?

NO

L3_PDE_reasoning

q0099

null

validity

If a system exhibits transient chaos but settles into a periodic orbit, should it still be classified as chaotic in steady state?

NO

L3_transient

q0100

null

hard

Does the existence of multiple positive Lyapunov exponents in Lorenz-96 necessarily imply hyperchaos?

NO

L3_hyperchaos